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plot_comparison(y_test, y_pred, 'Ordinary Linear Regression, Test Set')
import os
import numpy as np
import scipy.io
from sklearn import linear_model
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score, confusion_matrix, mean_squared_error, r2_score
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt
from IPython.display import clear_output
import random
import sys
After reading and preprocessing the data in the next code chunk, the data from all cells is stored in a population dictionary. The dictionary's keys correspond to the cell names, and the values contain the data for each respective cell.
The values in the population dictionary are cell dictionaries with keys being 'axons', 'green_dFFMeanValues',and 'red_dFFMeanValues':
'axons', e.g., cell_data_dict['CL090_230515']['axons'] is a 1 dimensional numpy array, of which the length is the number of groups and the elements are 1 dimensional numpy arrays consisting of components belonging to the group.'green_dFFMeanValues' is a 2 dimensional 3 by 49 numpy array (each cell has 3 rounds, and each round has 8 directions * 2 time frequencies * 3 space frequencies = 48 settings plus a extra period so in total there are 49 columns), of which the elements are still 2 dimensional numpy arrays with size being 10 by N (N is the number of components).'red_dFFMeanValues' is similarly a 2 dimensional 3 by 49 numpy array, of which the elements are still 2 dimensional numpy arrays with size being 10 by 1 (only recording the data at the soma).root_path = "/content/drive/MyDrive/Fluorescence_Data/FluoData4Fitting_Average"
# Get a list of all the subdirectories: subfolders are viewed as cell names
cell_names = [f for f in os.listdir(root_path) if os.path.isdir(os.path.join(root_path, f))]
# for cell in cell_names:
# print(cell)
# Create a dictionary with default values
default_value = 0
cell_data_dict = {cell: default_value for cell in cell_names}
# print(cell_data_dict)
file_suffixes = ['green_Axon.mat', 'green_dFFMeanValues.mat', 'red_dFFMeanValues.mat']
for cell in cell_names:
print(cell)
file_names = [cell + suffix for suffix in file_suffixes]
path_ = file_names[0] # green_Axon.mat
path_ = os.path.join(root_path, cell, path_)
mat_data = scipy.io.loadmat(path_)
axons = mat_data['Axons'] # array containing nested arrays/sub-arrays
# Squeeze the outer array
axons = np.squeeze(axons, axis=0)
for i in range(len(axons)):
# Squeeze the inner array and convert the data type to 'int'
axons[i] = np.squeeze(axons[i].astype(int), axis=0)
# final axons' length is the number of groups with
# each elements being a nested array of components
path_ = file_names[1] # green_dFFMeanValues.mat
path_ = os.path.join(root_path, cell, path_)
mat_data = scipy.io.loadmat(path_)
dFFMeanValues_green = mat_data['dFFMeanValues'] # 3 by 49
path_ = file_names[2] # red_dFFMeanValues.mat
path_ = os.path.join(root_path, cell, path_)
mat_data = scipy.io.loadmat(path_)
dFFMeanValues_red = mat_data['dFFMeanValues'] # 3 by 49
cell_data_dict[cell] = {'axons': axons,
'green_dFFMeanValues': dFFMeanValues_green,
'red_dFFMeanValues': dFFMeanValues_red}
# Print keys and types
for key, value in cell_data_dict.items():
print("-- * * * * * --")
print(key, type(value))
for key_, value_ in value.items():
print(key_, type(value_))
print("-- * * * * * --")
CL090_230515 CL090_230518 CL083_230413 CL075_230303 -- * * * * * -- CL090_230515 <class 'dict'> axons <class 'numpy.ndarray'> green_dFFMeanValues <class 'numpy.ndarray'> red_dFFMeanValues <class 'numpy.ndarray'> -- * * * * * -- CL090_230518 <class 'dict'> axons <class 'numpy.ndarray'> green_dFFMeanValues <class 'numpy.ndarray'> red_dFFMeanValues <class 'numpy.ndarray'> -- * * * * * -- CL083_230413 <class 'dict'> axons <class 'numpy.ndarray'> green_dFFMeanValues <class 'numpy.ndarray'> red_dFFMeanValues <class 'numpy.ndarray'> -- * * * * * -- CL075_230303 <class 'dict'> axons <class 'numpy.ndarray'> green_dFFMeanValues <class 'numpy.ndarray'> red_dFFMeanValues <class 'numpy.ndarray'> -- * * * * * --
# print to see data type and size
print(cell_data_dict['CL090_230515'].keys())
print(type(cell_data_dict['CL090_230515']['axons']))
print(cell_data_dict['CL090_230515']['axons'].shape)
print(cell_data_dict['CL090_230515']['axons'][1].shape)
print(cell_data_dict['CL090_230515']['axons'][1].dtype)
print("--------------------------------")
print(type(cell_data_dict['CL090_230515']['green_dFFMeanValues']))
print(cell_data_dict['CL090_230515']['green_dFFMeanValues'].shape)
print(type(cell_data_dict['CL090_230515']['green_dFFMeanValues'][1,1]))
print(cell_data_dict['CL090_230515']['green_dFFMeanValues'][0,1].shape)
print(cell_data_dict['CL083_230413']['green_dFFMeanValues'][0,1].shape)
print(cell_data_dict['CL083_230413']['green_dFFMeanValues'][0,1].dtype)
print("--------------------------------")
print(type(cell_data_dict['CL090_230515']['red_dFFMeanValues']))
print(cell_data_dict['CL090_230515']['red_dFFMeanValues'].shape)
print(type(cell_data_dict['CL090_230515']['red_dFFMeanValues'][1,1]))
print(cell_data_dict['CL090_230515']['red_dFFMeanValues'][0,1].shape)
print(cell_data_dict['CL083_230413']['red_dFFMeanValues'][0,1].shape)
print(cell_data_dict['CL083_230413']['red_dFFMeanValues'][0,1].dtype)
dict_keys(['axons', 'green_dFFMeanValues', 'red_dFFMeanValues']) <class 'numpy.ndarray'> (25,) (19,) int64 -------------------------------- <class 'numpy.ndarray'> (3, 49) <class 'numpy.ndarray'> (10, 281) (10, 155) float64 -------------------------------- <class 'numpy.ndarray'> (3, 49) <class 'numpy.ndarray'> (10, 1) (10, 2) float64
Note:
Four cells: 'CL090_230515', 'CL090_230518', 'CL083_230413', 'CL075_230303'.
'red_dFFMeanValues' and 'green_dFFMeanValues' have 49 columns,where the last column should be excluded. They are supposed to have 3 rows (3 rounds), but 'CL090_230518' only has 2 rows.
In 'CL083_230413', elements in 'red_dFFMeanValues' have 2 columns (10 × 2， should be 10 × 1), so 'CL083_230413' is not used.
def plot_comparison(y_test, y_pred, subtitle = ''):
# Sort y_pred and y_test based on y_test
sorted_indices = np.argsort(y_test)
sorted_y_pred = y_pred[sorted_indices]
sorted_y_test = y_test[sorted_indices]
# Plot sorted_y_pred and sorted_y_test
plt.plot(sorted_y_pred, label='Sorted Predictions')
plt.plot(sorted_y_test, label='Sorted Ground Truth')
plt.xlabel('Index')
plt.ylabel('Value')
plt.title(f'Comparison of Sorted Predictions and Sorted Ground Truth \n ({subtitle})')
plt.legend()
plt.savefig(f'Comparison ({subtitle}).png', bbox_inches='tight')
# bbox_inches='tight' will adjust the figure's bounding box to fit all the content, ensuring that
# the complete words are visible in the saved figure. Otherwise, the saved figure may not show the
# complete words, e.g., for x-label, or for the long title.
# The default setting can sometimes result in cutoff or clipped text. It tries to include the entire
# figure within the saved image, but there may be cases where the default behavior is not sufficient
# to capture all the content. The default behavior assumes the figure content fits within the predefined
# margins and padding.
plt.show()
# cell_data = cell_data_dict['CL090_230515']
cell_data = cell_data_dict['CL075_230303']
delete_small_group = True # delete groups (axons) with less than 3 components
data_green = cell_data['green_dFFMeanValues'][:,:-1] # exclude 49th column
data_red = cell_data['red_dFFMeanValues'][:,:-1] # exclude 49th column
data_axons = cell_data['axons']
# print(data_axons)
# print(type(data_axons),len(data_axons),data_axons)
if delete_small_group:
data_axons = np.array([axons_ for axons_ in data_axons if len(axons_) >= 3])
# print(type(data_axons),len(data_axons),data_axons)
# vstack green data
stacked_green = np.empty((0, data_green[0,0].shape[1]))
# Enumerate the elements in the np array and vstack them
for index, value in np.ndenumerate(data_green):
stacked_green = np.vstack((stacked_green, value))
print(stacked_green.shape, 48*3*10)
# group columns of green data
group_num = data_axons.shape[0]
group_satcked_green = np.zeros((stacked_green.shape[0], group_num))
for i, cols in enumerate(data_axons):
group_satcked_green[:, i] = np.sum(stacked_green[:, cols-1], axis=1)
print(group_satcked_green.shape, data_axons.shape)
# vstack red data
stacked_red = np.empty((0, data_red[0,0].shape[1]))
# Enumerate the elements in the np array and vstack them
for index, value in np.ndenumerate(data_red):
stacked_red = np.vstack((stacked_red, value))
print(stacked_red.shape, 48*3*10)
print(np.max(group_satcked_green), np.min(group_satcked_green))
print(np.max(stacked_red), np.min(stacked_red))
(1440, 80) 1440 (1440, 5) (5,) (1440, 1) 1440 27.44283678657392 -9.505092954427656 0.4404603811981394 -0.20703030293882338
<ipython-input-118-ddad8385ad7f>:12: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray. data_axons = np.array([axons_ for axons_ in data_axons if len(axons_) >= 3])
# independent data
x = group_satcked_green
# dependent data (labels/targets)
y = np.squeeze(stacked_red)
# Split the data into train and test sets
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.05, random_state=42)
print("x_train shape:", x_train.shape)
print("y_train shape:", y_train.shape)
print("x_test shape:", x_test.shape)
print("y_test shape:", y_test.shape)
x_train shape: (1368, 5) y_train shape: (1368,) x_test shape: (72, 5) y_test shape: (72,)
Ordinary least squares Linear Regression.
Linear Regression fits a linear model with coefficients to minimize the residual sum of squares between the observed targets in the dataset, and the targets predicted by the linear approximation.
# Create a LinearRegression object
model = linear_model.LinearRegression()
# Fit the model on the training data
model.fit(x_train, y_train)
# Print the fitted coefficients
print("Fitted Coefficients:", model.coef_)
# Print the fitted intercept
print("Fitted Intercept:", model.intercept_)
# Predict on the test data
y_pred = model.predict(x_test)
Fitted Coefficients: [ 0.02750133 0.00644773 0.01610286 -0.00245954 0.00325725] Fitted Intercept: 0.021384507405425024
mse = mean_squared_error(y_test, y_pred)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred, y_test)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test, y_pred)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
Mean squared error: 0.0021013740360479637 Correlation coefficient: 0.5516491307623594 Coefficient of determination (R-squared score, R2 score): 0.30412235302891344
plot_comparison(y_test, y_pred, 'Ordinary Linear Regression, Test Set')
# predict on train
# Use the trained model to make predictions
y_pred_ = model.predict(x_train)
mse = mean_squared_error(y_train, y_pred_)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred_, y_train)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train, y_pred_)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
Mean squared error: 0.0016130542307865325 Correlation coefficient: 0.5303604736894671 Coefficient of determination (R-squared score, R2 score): 0.2812822320521161
plot_comparison(y_train, y_pred_, 'Ordinary Linear Regression, Train Set')
# digitized results
print("---- ---- ----")
class_num = 16
# Calculate the minimum and maximum values
infinitesimal = np.finfo(float).eps
min_val = np.min(y) - infinitesimal # to guarantee to include min
max_val = np.max(y) + infinitesimal # to guarantee to include max
# Generate class_num+1 evenly spaced intervals
intervals = np.linspace(min_val, max_val, num=class_num+1) # num = class num + 1
y_train_digital = np.digitize(y_train, intervals) - 1
y_test_digital = np.digitize(y_test, intervals) - 1
y_pred_train_digital = np.digitize(y_pred_, intervals) - 1
y_pred_test_digital = np.digitize(y_pred, intervals) - 1
mse = mean_squared_error(y_test_digital, y_pred_test_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_test_digital, y_test_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test_digital, y_pred_test_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
mse = mean_squared_error(y_train_digital, y_pred_train_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_train_digital, y_train_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train_digital, y_pred_train_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
---- ---- ---- Mean squared error: 1.3611111111111112 Correlation coefficient: 0.5192778681631646 Coefficient of determination (R-squared score, R2 score): 0.2679738562091504 Mean squared error: 1.1140350877192982 Correlation coefficient: 0.47374351663713143 Coefficient of determination (R-squared score, R2 score): 0.21872132035869019
Linear least squares with l2 regularization.
Minimizes the objective function:
$$ ||y - Xw||^2_2 + \alpha ||w||^2_2 $$This model solves a regression model where the loss function is the linear least squares function and regularization is given by the l2-norm.
# Create a Ridge Regression object
ridge_model = linear_model.Ridge(alpha=1.0) # You can adjust the value of alpha as per your requirements
# Fit the model on the training data
ridge_model.fit(x_train, y_train)
# Print the fitted coefficients
print("Fitted Coefficients:", ridge_model.coef_)
# Print the fitted intercept
print("Fitted Intercept:", ridge_model.intercept_)
# Predict on the test data
y_pred = ridge_model.predict(x_test)
Fitted Coefficients: [ 0.02737809 0.00640785 0.01592334 -0.00242911 0.00326877] Fitted Intercept: 0.02141557952594624
mse = mean_squared_error(y_test, y_pred)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred, y_test)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test, y_pred)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
plot_comparison(y_test, y_pred, 'Ridge Linear Regression, Test Set')
Mean squared error: 0.0020998258646144365 Correlation coefficient: 0.5521413386329813 Coefficient of determination (R-squared score, R2 score): 0.30463503562410577
# predict on train
# Use the trained model to make predictions
y_pred_ = ridge_model.predict(x_train)
mse = mean_squared_error(y_train, y_pred_)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred_, y_train)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train, y_pred_)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
plot_comparison(y_train, y_pred_, 'Ridge Linear Regression, Train Set')
Mean squared error: 0.0016130590000993249 Correlation coefficient: 0.5303588713620216 Coefficient of determination (R-squared score, R2 score): 0.2812801070213643
# digitized results
print("---- ---- ----")
class_num = 16
# Calculate the minimum and maximum values
infinitesimal = np.finfo(float).eps
min_val = np.min(y) - infinitesimal # to guarantee to include min
max_val = np.max(y) + infinitesimal # to guarantee to include max
# Generate class_num+1 evenly spaced intervals
intervals = np.linspace(min_val, max_val, num=class_num+1) # num = class num + 1
y_train_digital = np.digitize(y_train, intervals) - 1
y_test_digital = np.digitize(y_test, intervals) - 1
y_pred_train_digital = np.digitize(y_pred_, intervals) - 1
y_pred_test_digital = np.digitize(y_pred, intervals) - 1
mse = mean_squared_error(y_test_digital, y_pred_test_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_test_digital, y_test_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test_digital, y_pred_test_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
mse = mean_squared_error(y_train_digital, y_pred_train_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_train_digital, y_train_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train_digital, y_pred_train_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
---- ---- ---- Mean squared error: 1.3611111111111112 Correlation coefficient: 0.5192778681631646 Coefficient of determination (R-squared score, R2 score): 0.2679738562091504 Mean squared error: 1.1103801169590644 Correlation coefficient: 0.47591543732849056 Coefficient of determination (R-squared score, R2 score): 0.22128457061998064
Linear regression with combined L1 and L2 priors as regularizer.
Minimizes the objective function:
$$ 1 / (2 * n_{samples}) * ||y - Xw||^2_2 + \alpha * l1_{ratio} * ||w||_1 + 0.5 * \alpha * (1 - l1_{ratio}) * ||w||^2_2 $$If controlling the L1 and L2 penalty separately, that this is equivalent to:
$$ a * ||w||_1 + 0.5 * b * ||w||_2^2 $$where: $\alpha = a + b$ and $l1_{ratio} = a / (a + b)$.
# Create an ElasticNet object
a = 0.004; b = 0.00
alpha = a + b; l1_ratio = a / (a + b)
elasticnet_model = linear_model.ElasticNet(alpha=alpha, l1_ratio=l1_ratio, max_iter=100000)
# adjust the values of alpha and l1_ratio as per your requirements
# Fit the model on the training data
elasticnet_model.fit(x_train, y_train)
# Print the fitted coefficients
print("Fitted Coefficients:", elasticnet_model.coef_)
# Print the fitted intercept
print("Fitted Intercept:", elasticnet_model.intercept_)
# Predict on the test data
y_pred = elasticnet_model.predict(x_test)
# It is normal to encounter warning here, because our data is not linear enough
# and not normailized to guarantee a low error/residual, even though we set a very
# large max_iter. But the results is similar to that of ordinary and Ridge linear
# regression. Like alpha = 0 results in the same results as the ordinary linear
# rergession.
Fitted Coefficients: [0.00866444 0. 0. 0.00158259 0.0047032 ] Fitted Intercept: 0.022844047405427618
mse = mean_squared_error(y_test, y_pred)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred, y_test)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test, y_pred)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
plot_comparison(y_test, y_pred, 'Elasticnet Linear Regression, Test Set')
Mean squared error: 0.0020020605564851465 Correlation coefficient: 0.6136634710485406 Coefficient of determination (R-squared score, R2 score): 0.33701037262235
# predict on train
# Use the trained model to make predictions
y_pred_ = elasticnet_model.predict(x_train)
mse = mean_squared_error(y_train, y_pred_)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred_, y_train)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train, y_pred_)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
plot_comparison(y_train, y_pred_, 'Elasticnet Linear Regression, Train Set')
Mean squared error: 0.0016981988382008856 Correlation coefficient: 0.4970722873576219 Coefficient of determination (R-squared score, R2 score): 0.2433449197003772
# digitized results
print("---- ---- ----")
class_num = 16
# Calculate the minimum and maximum values
infinitesimal = np.finfo(float).eps
min_val = np.min(y) - infinitesimal # to guarantee to include min
max_val = np.max(y) + infinitesimal # to guarantee to include max
# Generate class_num+1 evenly spaced intervals
intervals = np.linspace(min_val, max_val, num=class_num+1) # num = class num + 1
y_train_digital = np.digitize(y_train, intervals) - 1
y_test_digital = np.digitize(y_test, intervals) - 1
y_pred_train_digital = np.digitize(y_pred_, intervals) - 1
y_pred_test_digital = np.digitize(y_pred, intervals) - 1
mse = mean_squared_error(y_test_digital, y_pred_test_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_test_digital, y_test_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test_digital, y_pred_test_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
mse = mean_squared_error(y_train_digital, y_pred_train_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_train_digital, y_train_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train_digital, y_pred_train_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
---- ---- ---- Mean squared error: 1.3472222222222223 Correlation coefficient: 0.5463431384225381 Coefficient of determination (R-squared score, R2 score): 0.2754435107376284 Mean squared error: 1.1359649122807018 Correlation coefficient: 0.4511357285754583 Coefficient of determination (R-squared score, R2 score): 0.20334181879094793
Mathematically, a power-law relationship can be expressed as:
$$ y = A X^C $$Here, I modify it, shown as:
$$ y = A (X+B)^C + D $$where, $X = \beta_1 x_1 + \beta_2 x_2 \dots + \beta_N x_N$. $X+D$ is a linear regression part. $A$, $B$, $C$, $D$, $\beta_1$, $\beta_2$, ...,$\beta_N$ are parameters to be determined.
# independent data
x = group_satcked_green
# dependent data (labels/targets)
y = np.squeeze(stacked_red)
# Split the data into train and test sets
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.05, random_state=42)
print("x_train shape:", x_train.shape)
print("y_train shape:", y_train.shape)
print("x_test shape:", x_test.shape)
print("y_test shape:", y_test.shape)
x_train shape: (1368, 5) y_train shape: (1368,) x_test shape: (72, 5) y_test shape: (72,)
exponent = 5
# Define the model function
def func(X, *params):
A, B, D = params[:3]
# Compute the weighted sum
weighted_sum = np.sum(X * np.array(params[3:]), axis=1)
base = weighted_sum + B
power_result = np.power(base, exponent)
return A * power_result + D
# Create a LinearRegression object
model = linear_model.LinearRegression()
# give the initial params using linear regression
# so that the params are within a reasonable range
model.fit(x_train, y_train)
# print("Fitted Coefficients:", model.coef_)
# print("Fitted Intercept:", model.intercept_)
num_features = x_train.shape[1]
# Assuming model.coef_ is the np array containing the coefficients
model_coefs = model.coef_
# Set negative elements to 0 using np.clip()
initial_params = [1, model.intercept_, 0] + list(model_coefs) # Initial parameter guesses
# model_coefs_clipped = np.clip(model_coefs, 0, np.inf)
# initial_params = [1, model.intercept_, 0] + list(model_coefs_clipped) # Initial parameter guesses, no need to clip -- they can be negative
# Set lower and upper bounds for the parameters
lower_bounds = [0, -np.inf, -np.inf] + [0] * num_features
upper_bounds = [np.inf, np.inf, np.inf] + [np.inf] * num_features
# Combine the lower and upper bounds into a 2-tuple of array_like
bounds = (lower_bounds, upper_bounds)
# Perform the curve fit with bounds
params, params_covariance = curve_fit(func, x_train, y_train, p0=initial_params, maxfev=1000000)
# params, params_covariance = curve_fit(func, x_train, y_train, p0=initial_params, bounds=bounds, maxfev=1000000)
# Print the fitted parameters
print("Fitted Parameters:", params)
# predict on test
A, B, D = params[:3]
weighted_sum = np.sum(x_test * np.array(params[3:]), axis=1)
base = weighted_sum + B
abs_base = np.abs(base)
sign = np.sign(base)
power_result = np.power(abs_base, exponent)
y_pred = A * sign * power_result + D
mse = mean_squared_error(y_test, y_pred)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred, y_test)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test, y_pred)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
plot_comparison(y_test, y_pred, 'Power-Law Regression Exponent=5, Test Set')
# predict on train
A, B, D = params[:3]
weighted_sum = np.sum(x_train * np.array(params[3:]), axis=1)
base = weighted_sum + B
abs_base = np.abs(base)
sign = np.sign(base)
power_result = np.power(abs_base, exponent)
y_pred_ = A * sign * power_result + D
mse = mean_squared_error(y_train, y_pred_)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred_, y_train)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train, y_pred_)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
plot_comparison(y_train, y_pred_, 'Power-Law Regression (Exponent=5), Train Set')
# digitized results
print("---- ---- ----")
class_num = 16
# Calculate the minimum and maximum values
infinitesimal = np.finfo(float).eps
min_val = np.min(y) - infinitesimal # to guarantee to include min
max_val = np.max(y) + infinitesimal # to guarantee to include max
# Generate class_num+1 evenly spaced intervals
intervals = np.linspace(min_val, max_val, num=class_num+1) # num = class num + 1
y_train_digital = np.digitize(y_train, intervals) - 1
y_test_digital = np.digitize(y_test, intervals) - 1
y_pred_train_digital = np.digitize(y_pred_, intervals) - 1
y_pred_test_digital = np.digitize(y_pred, intervals) - 1
mse = mean_squared_error(y_test_digital, y_pred_test_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_test_digital, y_test_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test_digital, y_pred_test_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
mse = mean_squared_error(y_train_digital, y_pred_train_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_train_digital, y_train_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train_digital, y_pred_train_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
Fitted Parameters: [ 1.18600565e+01 3.44121000e-01 -4.05562036e-02 2.77702818e-02 2.47117908e-03 2.09451252e-02 -2.56362694e-03 3.66822262e-03] Mean squared error: 0.0026229360598610057 Correlation coefficient: 0.47446924924518413 Coefficient of determination (R-squared score, R2 score): 0.13140519384906468
Mean squared error: 0.001563847057598201 Correlation coefficient: 0.550642481932762 Coefficient of determination (R-squared score, R2 score): 0.30320714257648085
---- ---- ---- Mean squared error: 1.7083333333333333 Correlation coefficient: 0.45098751419685795 Coefficient of determination (R-squared score, R2 score): 0.08123249299719892 Mean squared error: 1.1001461988304093 Correlation coefficient: 0.4832959693241634 Coefficient of determination (R-squared score, R2 score): 0.22846167135159368
# compared with example 1, here only fit A and D.
exponent = 5
model = linear_model.LinearRegression()
model.fit(x_train, y_train)
# now we have: model.intercept_ and model.coef_
# Print the fitted coefficients
print("Fitted Coefficients:", model.coef_)
# Print the fitted intercept
print("Fitted Intercept:", model.intercept_)
# Define the model function
def func(X, A, D):
# Compute the weighted sum
weighted_sum = np.sum(X * np.array(model.coef_), axis=1)
base = weighted_sum
power_result = np.power(base, exponent)
return A * power_result + D
initial_params = [1, 0]
# Perform the curve fit
params, params_covariance = curve_fit(func, x_train, y_train, p0=initial_params, maxfev=1000000)
# Print the fitted parameters
print("Fitted Parameters:", params)
# predict on test
A, D = params
y_pred = func(x_test, A, D)
mse = mean_squared_error(y_test, y_pred)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred, y_test)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test, y_pred)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
plot_comparison(y_test, y_pred, 'Power-Law Regression Exponent=5, only fit A and D, Test Set')
# predict on train
A, D = params
y_pred_ = func(x_train, A, D)
mse = mean_squared_error(y_train, y_pred_)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred_, y_train)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train, y_pred_)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
plot_comparison(y_train, y_pred_, 'Power-Law Regression Exponent=5, only fit A and D, Train Set')
Fitted Coefficients: [ 0.02750133 0.00644773 0.01610286 -0.00245954 0.00325725] Fitted Intercept: 0.021384507405425024 Fitted Parameters: [4.05181437e+03 1.77237254e-02] Mean squared error: 0.005299362470883888 Correlation coefficient: 0.2996981978301417 Coefficient of determination (R-squared score, R2 score): -0.7549031364359122
Mean squared error: 0.001978769231784402 Correlation coefficient: 0.3439957106418279 Coefficient of determination (R-squared score, R2 score): 0.1183330489399761
# generate irreducible fraction with an odd number as the denominator
# such numbers can work as the exponent for negative numbers and
# will be used as the parameter "C" in Power-law regression below:
# y = A * (B+b1*x1+b2*x2+...+bN*xN)**C + D
def gcd(a, b): # calculate the greatest common divisor of two numbers
while b:
a, b = b, a % b
return a
def generate_irreducible_fraction(existing_fractions = []):
while True:
numerator = random.randint(1, 400) # Random numerator
denominator = random.randrange(1, 100, 2) # Random odd denominator
if gcd(numerator, denominator) == 1: # Check if the fraction is irreducible
fraction = (numerator, denominator)
if fraction not in existing_fractions: # Check if the fraction is not a duplicate
return fraction
# Generate irreducible fraction numbers
N_faction = 40
upper_bound = 50
irreducible_fractions = []
while len(irreducible_fractions) < N_faction:
fraction = generate_irreducible_fraction(irreducible_fractions)
if fraction[0]/fraction[1] < upper_bound:
irreducible_fractions.append(fraction)
# Sort the irreducible fractions
irreducible_fractions.sort(key=lambda f: f[0] / f[1])
# Print the irreducible fraction numbers
for numerator, denominator in irreducible_fractions:
if random.random() <= 0.1:
print(f"{numerator}/{denominator}")
# Extract the numerator and denominator values
indexes = range(1, len(irreducible_fractions) + 1)
values = [numerator / denominator for numerator, denominator in irreducible_fractions]
# Plot the irreducible fractions
plt.plot(values, 'o-')
plt.xlabel("Index")
plt.ylabel("Irreducible Fraction")
plt.title("Irreducible Fractions")
plt.show()
## if not use the above random generated irreducible_fractions, define it below.
irreducible_fractions = [(1,95), (30,43), (179,65), (5,1), (221,33), (219,23), (300,17), (73,3)]
158/99 63/17 87/11 390/43
# # old code! The new one is in the next chunk.
# params_list = []
# for numerator, denominator in irreducible_fractions:
# C1, C2 = numerator, denominator
# # Define the model function
# def func(X, *params):
# A, B, D = params[:3]
# # Compute the weighted sum
# weighted_sum = np.sum(X * np.array(params[3:]), axis=1)
# base = weighted_sum + B
# abs_base = np.abs(base)
# sign = np.sign(base)
# power_result = np.power(abs_base, C1 / C2)
# return A * sign * power_result + D
# # Create a LinearRegression object
# model = linear_model.LinearRegression()
# # give the initial params using linear regression
# # so that the params are within a reasonable range
# model.fit(x_train, y_train)
# # print("Fitted Coefficients:", model.coef_)
# # print("Fitted Intercept:", model.intercept_)
# num_features = x_train.shape[1]
# initial_params = [1, model.intercept_, 0] + list(model.coef_) # Initial parameter guesses
# # Perform the curve fit
# params, params_covariance = curve_fit(func, x_train, y_train, p0=initial_params, maxfev=1000000)
# params_list.append(params)
# # Print the fitted parameters
# # print("Fitted Parameters:", params)
# # predict on test
# y_predict_test_list = []
# for (numerator, denominator), params in zip(irreducible_fractions, params_list):
# C1, C2 = numerator, denominator
# A, B, D = params[:3]
# weighted_sum = np.sum(x_test * np.array(params[3:]), axis=1)
# base = weighted_sum + B
# abs_base = np.abs(base)
# sign = np.sign(base)
# power_result = np.power(abs_base, C1 / C2)
# y_pred = A * sign * power_result + D
# y_predict_test_list.append(y_pred)
# # predict on train
# y_predict_train_list = []
# for (numerator, denominator), params in zip(irreducible_fractions, params_list):
# C1, C2 = numerator, denominator
# A, B, D = params[:3]
# weighted_sum = np.sum(x_train * np.array(params[3:]), axis=1)
# base = weighted_sum + B
# abs_base = np.abs(base)
# sign = np.sign(base)
# power_result = np.power(abs_base, C1 / C2)
# y_pred_ = A * sign * power_result + D
# y_predict_train_list.append(y_pred_)
# new code, a updated version for the code in last chunk.
# input and output data normalization is achieved (but it
# seems normalization is redundant).
class CurveFit_with_Normalization:
def __init__(self, exponent_numerator=1, exponent_denominator=1, input_range=[1,2], output_range=[1,2]):
self.input_min = input_range[0]
self.input_max = input_range[1]
self.output_min = output_range[0]
self.output_max = output_range[1]
self.input_scale = None
self.input_shift = None
self.output_scale = None
self.output_shift = None
self.exponent_numerator = exponent_numerator
self.exponent_denominator = exponent_denominator
self.linear_model = linear_model.LinearRegression()
def fit(self, X, y):
# Normalize the input and output data
self.input_scale = (self.input_max - self.input_min) / (np.max(X) - np.min(X))
self.input_shift = self.input_min - np.min(X) * self.input_scale
normalized_X = self.input_scale * X + self.input_shift
self.output_scale = (self.output_max - self.output_min) / (np.max(y) - np.min(y))
self.output_shift = self.output_min - np.min(y) * self.output_scale
normalized_y = self.output_scale * y + self.output_shift
def normalized_func_(X_normalize, *params):
A, B, D = params[:3]
# Compute the weighted sum
weighted_sum = np.sum(X_normalize * np.array(params[3:]), axis=1)
base = weighted_sum + B
abs_base = np.abs(base)
sign = np.sign(base)
power_result = np.power(abs_base, self.exponent_numerator / self.exponent_denominator)
return A * sign * power_result + D
# Give the initial params using linear regression
self.linear_model.fit(normalized_X, normalized_y)
# print("Fitted Coefficients:", linear_model.coef_)
# print("Fitted Intercept:", linear_model.intercept_)
# num_features = X.shape[1]
exponent = self.exponent_numerator / self.exponent_denominator
initial_params = [1, self.linear_model.intercept_ / exponent + (1 - 1 / exponent), 0] + list(self.linear_model.coef_ /
exponent) # Initial parameter guesses
# initial_params = [1, 0, 0] + [1 / X.shape[1]] * (X.shape[1])
# Perform the normalized curve fit
normalized_params, params_covariance = curve_fit(normalized_func_, normalized_X, normalized_y,
p0=initial_params, maxfev=100000000)
# Store the fitted parameters
self.normalized_fitted_params = normalized_params
def predict(self, X):
# Normalize the input data using the previously calculated scaling and shifting parameters
normalized_X = self.input_scale * X + self.input_shift
# Make predictions using the denormalized parameters
y_pred = self.normalized_func(normalized_X, self.exponent_numerator,
self.exponent_denominator, *self.normalized_fitted_params)
# Denormalize the predicted output
y_pred = (y_pred - self.output_shift) / self.output_scale
return y_pred
@staticmethod
def normalized_func(X_normalize, exponent_numerator, exponent_denominator, *params):
A, B, D = params[:3]
# Compute the weighted sum
weighted_sum = np.sum(X_normalize * np.array(params[3:]), axis=1)
base = weighted_sum + B
abs_base = np.abs(base)
sign = np.sign(base)
power_result = np.power(abs_base, exponent_numerator / exponent_denominator)
return A * sign * power_result + D
model_list = []
for numerator, denominator in irreducible_fractions:
# Create an instance of NormalizedCurveFit
model = CurveFit_with_Normalization(numerator, denominator, input_range=[1, 2], output_range=[1, 2])
# Fit the model to your input and output data
model.fit(x_train, y_train)
model_list.append(model)
# this is for the new version code in the last chunk
r2_score_test_list = []
# predict on test
y_predict_test_list = []
for model, (numerator, denominator) in zip(model_list, irreducible_fractions):
y_pred = model.predict(x_test)
print(f'-------- \n (numerator, denominator) is: ({numerator}, {denominator})')
mse = mean_squared_error(y_test, y_pred)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred, y_test)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test, y_pred)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
r2_score_test_list.append(r_squared)
y_predict_test_list.append(y_pred)
print("|||||||||||||||||||||||||||||||||||||")
r2_score_train_list = []
# predict on train
y_predict_train_list = []
for model, (numerator, denominator) in zip(model_list, irreducible_fractions):
y_pred_ = model.predict(x_train)
print(f'-------- \n (numerator, denominator) is: ({numerator}, {denominator})')
mse = mean_squared_error(y_train, y_pred_)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred_, y_train)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train, y_pred_)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
r2_score_train_list.append(r_squared)
y_predict_train_list.append(y_pred_)
x = [numerator / denominator for (numerator, denominator) in irreducible_fractions]
# plot the r2 score curve over exponent
fig, ax = plt.subplots(figsize=(7.5, 5)) # Adjust the values as desired
# Plot the R-squared scores
ax.plot(x, r2_score_train_list, label='Train R-squared')
ax.plot(x, r2_score_test_list, label='Test R-squared')
# Set labels and title with font size
ax.set_xlabel('Exponent in Power Law', fontsize=14)
ax.set_ylabel('R-squared', fontsize=14)
ax.set_title('R-squared Scores', fontsize=16)
# Set tick label font size
ax.tick_params(axis='x', labelsize=12)
ax.tick_params(axis='y', labelsize=12)
# Set legend
ax.legend(fontsize=12)
fig.savefig('Power_Law_r2_scores_plot.png')
# Display the plot
plt.show()
-------- (numerator, denominator) is: (1, 95) Mean squared error: 0.002100964640127741 Correlation coefficient: 0.5517910432357731 Coefficient of determination (R-squared score, R2 score): 0.3042579259753555 -------- (numerator, denominator) is: (30, 43) Mean squared error: 0.002101281865505407 Correlation coefficient: 0.5516808169870028 Coefficient of determination (R-squared score, R2 score): 0.30415287563896487 -------- (numerator, denominator) is: (179, 65) Mean squared error: 0.0025250507543628977 Correlation coefficient: 0.4832436056815392 Coefficient of determination (R-squared score, R2 score): 0.16382026841198005 -------- (numerator, denominator) is: (5, 1) Mean squared error: 0.0026225156812671405 Correlation coefficient: 0.47450623106504053 Coefficient of determination (R-squared score, R2 score): 0.13154440374778698 -------- (numerator, denominator) is: (221, 33) Mean squared error: 0.0026499746952767882 Correlation coefficient: 0.4722949272041147 Coefficient of determination (R-squared score, R2 score): 0.12245125149150604 -------- (numerator, denominator) is: (219, 23) Mean squared error: 0.0026738709969947676 Correlation coefficient: 0.47042871941472747 Coefficient of determination (R-squared score, R2 score): 0.1145379043550332 -------- (numerator, denominator) is: (300, 17) Mean squared error: 0.002698617492593064 Correlation coefficient: 0.4685731269373298 Coefficient of determination (R-squared score, R2 score): 0.10634301242607913 -------- (numerator, denominator) is: (73, 3) Mean squared error: 0.0027064284283282954 Correlation coefficient: 0.46800240398942017 Coefficient of determination (R-squared score, R2 score): 0.10375639267784165 ||||||||||||||||||||||||||||||||||||| -------- (numerator, denominator) is: (1, 95) Mean squared error: 0.0016134189436037255 Correlation coefficient: 0.530207263618693 Coefficient of determination (R-squared score, R2 score): 0.2811197294053285 -------- (numerator, denominator) is: (30, 43) Mean squared error: 0.0016131201665299491 Correlation coefficient: 0.5303327777597914 Coefficient of determination (R-squared score, R2 score): 0.28125285350461793 -------- (numerator, denominator) is: (179, 65) Mean squared error: 0.001564363067723666 Correlation coefficient: 0.5504336724006264 Coefficient of determination (R-squared score, R2 score): 0.3029772274015695 -------- (numerator, denominator) is: (5, 1) Mean squared error: 0.0015638470628401345 Correlation coefficient: 0.5506424830440508 Coefficient of determination (R-squared score, R2 score): 0.3032071402408676 -------- (numerator, denominator) is: (221, 33) Mean squared error: 0.0015638033309179715 Correlation coefficient: 0.550660172508143 Coefficient of determination (R-squared score, R2 score): 0.30322662558047075 -------- (numerator, denominator) is: (219, 23) Mean squared error: 0.0015637917943133492 Correlation coefficient: 0.5506648398692617 Coefficient of determination (R-squared score, R2 score): 0.30323176586810985 -------- (numerator, denominator) is: (300, 17) Mean squared error: 0.0015638010388691812 Correlation coefficient: 0.5506610998555096 Coefficient of determination (R-squared score, R2 score): 0.30322764683329595 -------- (numerator, denominator) is: (73, 3) Mean squared error: 0.0015638079818543363 Correlation coefficient: 0.5506582908609674 Coefficient of determination (R-squared score, R2 score): 0.30322455329391074
# for model in model_list:
# print(model.exponent_numerator, model.exponent_denominator)
# both the old and new versions (in the last subsection "Fit and predict") of code
# share the same evaluate code in this subsectoon.
# Create and update multiple figures (test)
for y_pred, (numerator, denominator) in zip(y_predict_test_list, irreducible_fractions):
plot_comparison(y_test, y_pred, f'Power-Law Regression Exponent={numerator} over {denominator}, Test Set')
# here pay attention: cannot use / replace over in the name, otherwise cannot save the fig
# because / cannot be in a file name.
print(y_pred[0])
clear_output(wait=True) # Clear the previous output
-0.0068363855310673224
# Create and update multiple figures (train)
for y_pred_, (numerator, denominator) in zip(y_predict_train_list, irreducible_fractions):
plot_comparison(y_train, y_pred_, f'Power-Law Regression Exponent={numerator} over {denominator}, Train Set')
print(y_pred_[0])
clear_output(wait=True) # Clear the previous output
-0.006264150549880837
Let $B = (b_1, b_2, \ldots , b_N)$. $$ y = A \cdot e^{(b_1 \cdot x_1 + \ldots + b_N \cdot x_N)} + C $$
# independent data
x = group_satcked_green
# dependent data (labels/targets)
y = np.squeeze(stacked_red)
# Split the data into train and test sets
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.05, random_state=42)
print("x_train shape:", x_train.shape)
print("y_train shape:", y_train.shape)
print("x_test shape:", x_test.shape)
print("y_test shape:", y_test.shape)
x_train shape: (1368, 5) y_train shape: (1368,) x_test shape: (72, 5) y_test shape: (72,)
# Define the model function
def func(X, *params):
A, C = params[:2]
return A * np.exp(np.sum(X * np.array(params[2:]), axis=1)) + C
# give the initial params using linear regression
# so that the params are within a reasonable range
num_features = x_train.shape[1]
initial_params = [np.mean(y_train), 0] + [0] * num_features # Initial parameter guesses
# Perform the curve fit
params, params_covariance = curve_fit(func, x_train, y_train, p0=initial_params, maxfev=1000000)
# Print the fitted parameters
print("Fitted Parameters:", params)
# predict on test
A, C = params[:2]
y_pred = A * np.exp(np.sum(x_test * np.array(params[2:]), axis=1)) + C
mse = mean_squared_error(y_test, y_pred)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred, y_test)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test, y_pred)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
# predict on train
A, C = params[:2]
y_pred_ = A * np.exp(np.sum(x_train * np.array(params[2:]), axis=1)) + C
mse = mean_squared_error(y_train, y_pred_)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred_, y_train)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train, y_pred_)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
r2_score_train_list.append(r_squared)
# digitized results
print("---- ---- ----")
class_num = 16
# Calculate the minimum and maximum values
infinitesimal = np.finfo(float).eps
min_val = np.min(y) - infinitesimal # to guarantee to include min
max_val = np.max(y) + infinitesimal # to guarantee to include max
# Generate class_num+1 evenly spaced intervals
intervals = np.linspace(min_val, max_val, num=class_num+1) # num = class num + 1
y_train_digital = np.digitize(y_train, intervals) - 1
y_test_digital = np.digitize(y_test, intervals) - 1
y_pred_train_digital = np.digitize(y_pred_, intervals) - 1
y_pred_test_digital = np.digitize(y_pred, intervals) - 1
print(y_pred)
print(y_pred_test_digital)
mse = mean_squared_error(y_test_digital, y_pred_test_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_test_digital, y_test_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test_digital, y_pred_test_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
mse = mean_squared_error(y_train_digital, y_pred_train_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_train_digital, y_train_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train_digital, y_pred_train_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
Fitted Parameters: [ 0.07779241 -0.06104678 0.29536653 0.02428094 0.22627202 -0.02735473 0.03966839] Mean squared error: 0.002726635527392822 Correlation coefficient: 0.466554602832389 Coefficient of determination (R-squared score, R2 score): 0.09706473840405994 Mean squared error: 0.0015638339543745966 Correlation coefficient: 0.5506477829720628 Coefficient of determination (R-squared score, R2 score): 0.3032129808920452 ---- ---- ---- [-0.00689957 -0.00666178 0.01360607 0.00661662 0.00731099 0.02449375 0.01326078 0.03334951 0.00512768 0.03277946 0.00727101 0.01555067 0.12159638 0.01786017 0.01402178 0.02199172 0.01459452 0.01422314 0.01935669 -0.00708446 0.03325915 0.0069828 0.00489899 0.01448913 0.00301878 0.35765372 0.00477497 0.02670886 0.01733475 -0.01236122 0.01620576 0.02950386 -0.00751631 0.0071461 0.0206256 0.00699687 0.01942845 0.03431444 0.01141902 0.02229449 0.0212914 -0.01130567 0.02393423 0.01708261 0.03761861 0.01389856 0.00729412 0.01502123 0.00753736 0.10468944 0.02559665 0.01614424 0.02416139 0.020876 0.01015729 0.00617441 0.01281935 0.00533284 0.01605946 0.02546893 0.01672694 0.01258805 0.01521004 -0.00640577 -0.00895642 0.01126611 0.02573762 0.01152167 -0.00115906 0.00837762 0.0270282 0.03119955] [ 4 4 5 5 5 5 5 5 5 5 5 5 8 5 5 5 5 5 5 4 5 5 5 5 5 13 5 5 5 4 5 5 4 5 5 5 5 5 5 5 5 4 5 5 6 5 5 5 5 7 5 5 5 5 5 5 5 5 5 5 5 5 5 4 4 5 5 5 5 5 5 5] Mean squared error: 1.7083333333333333 Correlation coefficient: 0.45098751419685795 Coefficient of determination (R-squared score, R2 score): 0.08123249299719892 Mean squared error: 1.1008771929824561 Correlation coefficient: 0.48299619891345313 Coefficient of determination (R-squared score, R2 score): 0.22794902129933559
plot_comparison(y_test, y_pred, 'Exponential Regression, Test Set')
plot_comparison(y_train, y_pred_, 'Exponential Regression, Train Set')
# independent data
x = group_satcked_green
class_num = 480
# dependent data (labels/targets)
y = np.squeeze(stacked_red)
# print(np.max(y), np.min(y))
# Split the data into train and test sets
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.05, random_state=42)
# Calculate the minimum and maximum values
infinitesimal = np.finfo(float).eps
min_val = np.min(y) - infinitesimal # to guarantee to include min
max_val = np.max(y) + infinitesimal # to guarantee to include max
# Generate class_num+1 evenly spaced intervals
intervals = np.linspace(min_val, max_val, num=class_num+1) # num = class num + 1
# print(intervals)
# Digitize the array to get the indices of the intervals
y_train = np.digitize(y_train, intervals) - 1
y_test = np.digitize(y_test, intervals) - 1
print("x_train shape:", x_train.shape)
print("y_train shape:", y_train.shape)
print("x_test shape:", x_test.shape)
print("y_test shape:", y_test.shape)
# to see unique elements (see if we have all 0, 1,..., class_num-1 classes, better close to all)
unique_elements = np.unique(y_train)
print("Unique elements:", unique_elements)
print("Number of unique elements:", len(unique_elements))
x_train shape: (1368, 5) y_train shape: (1368,) x_test shape: (72, 5) y_test shape: (72,) Unique elements: [ 65 71 72 75 79 80 85 88 91 94 95 99 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 244 245 248 250 252 255 256 257 259 260 262 265 268 269 270 274 278 297 304 335 341 346 350 353 357 378 429 479] Number of unique elements: 180
'multinomial' (default option for multi-calss) achieves better performance than 'ovr'.
# fit
model = linear_model.LogisticRegression(fit_intercept=True, max_iter=1000, multi_class='multinomial')
# model = linear_model.LogisticRegression(fit_intercept=True, max_iter=1000, multi_class='ovr')
fit_result = model.fit(x_train, y_train)
print(fit_result.intercept_.shape, fit_result.coef_.shape)
# print("Coefficients:", model.coef_[0,:])
# print("Intercept:", model.intercept_[0])
print('--- --- ---')
# predict
# Use the trained model to make predictions
y_pred = model.predict(x_test)
# Alternatively, you can get the predicted probabilities for each class
y_prob = model.predict_proba(x_test)
print('y_prob.shape:', y_prob.shape)
print(np.sum(y_prob, axis = 1))
# print(y_prob[0,:])
# Print the predicted class labels
print('y_pred:', y_pred)
print('y_test:', y_test)
print('y_pred shape:', y_pred.shape, 'y_test shape:', y_test.shape)
# Print the predicted probabilities
# print(y_prob)
(180,) (180, 5) --- --- --- y_prob.shape: (72, 180) [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.] y_pred: [162 141 167 152 162 170 168 166 162 170 152 169 260 138 167 170 157 173 162 99 166 152 162 163 162 378 152 190 140 162 162 166 162 162 190 140 150 180 162 166 157 147 166 170 163 166 152 138 162 202 190 162 190 166 174 190 171 162 190 170 162 162 190 140 147 162 158 138 162 158 199 184] y_test: [153 188 169 125 156 138 190 188 168 182 167 158 261 179 183 152 126 170 256 0 170 174 159 138 146 263 183 164 139 139 161 172 145 151 135 122 141 181 173 166 188 125 172 307 193 155 156 180 151 275 143 177 172 162 178 156 153 148 165 177 219 146 169 175 157 190 136 79 202 170 163 181] y_pred shape: (72,) y_test shape: (72,)
In previous data division, I classify data into class_num (e.g., class_num = 160) intervals (histogram, by np.digitize). Here, evaluate the results with the same number of classes (e.g., class_num = 160).
accuracy = accuracy_score(y_test, y_pred)
print("Accuracy:", accuracy)
# cm = confusion_matrix(y_test, y_pred)
# print("Confusion Matrix:") # y_test doesn't include all classes, so confusion matrix is less than num_class by num_class
# print(cm)
# the columns represent the predicted labels (predictions)
# the rows represent the true labels (ground truth)
# Predicted Class
# | Class 1 | Class 2 | Class 3 |
# -----------------------------------------------------
# True Class | TP1 | FN1 | FN1 |
# -----------------------------------------------------
# True Class | FP2 | TP2 | FN2 |
# -----------------------------------------------------
# True Class | FN3 | FP3 | TP3 |
mse = mean_squared_error(y_test, y_pred)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred, y_test)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test, y_pred)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
# Sort y_pred and y_test based on y_test
plot_comparison(y_test, y_pred, 'Logistic Linear Regression, Test Set')
Accuracy: 0.013888888888888888 Mean squared error: 1318.5694444444443 Correlation coefficient: 0.5212639786009838 Coefficient of determination (R-squared score, R2 score): 0.20414204593680674
# predict on train
# Use the trained model to make predictions
y_pred_ = model.predict(x_train)
# Alternatively, you can get the predicted probabilities for each class
y_prob_ = model.predict_proba(x_train)
accuracy = accuracy_score(y_train, y_pred_)
print("Accuracy:", accuracy)
# cm = confusion_matrix(y_train, y_pred_)
# print("Confusion Matrix:")
# print(cm)
# the columns represent the predicted labels (predictions)
# the rows represent the true labels (ground truth)
# Predicted Class
# | Class 1 | Class 2 | Class 3 |
# -----------------------------------------------------
# True Class | TP1 | FN1 | FN1 |
# -----------------------------------------------------
# True Class | FP2 | TP2 | FN2 |
# -----------------------------------------------------
# True Class | FN3 | FP3 | TP3 |
mse = mean_squared_error(y_train, y_pred_)
print("Mean squared error:", mse)
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred_, y_train)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train, y_pred_)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
plot_comparison(y_train, y_pred_, 'Logistic Linear Regression, Train Set')
Accuracy: 0.04751461988304093 Mean squared error: 1031.3523391812867 Correlation coefficient: 0.504515155991152 Coefficient of determination (R-squared score, R2 score): 0.16281542471269117
The model is based on classifying data into class_num (e.g., class_num = 160) intervals (histogram, by np.digitize). Here, evaluate the results a smaller number of classes (e.g., reduced_class_num = 16), that is, for the example of class_num = 160 and reduced_class_num = 16, classes 0, 1, ..., 15 become one class, i.e., 0; ...; classes 144, 145, ..., 159 become one class, i.e., 15.
print("---- ---- ----")
# Define the boundaries for digitization
reduced_class_num = 16
intervals = np.arange(0, class_num + 1, class_num / reduced_class_num)
print(intervals)
y_train_digital = np.digitize(y_train, intervals) - 1
y_test_digital = np.digitize(y_test, intervals) - 1
y_pred_train_digital = np.digitize(y_pred_, intervals) - 1
y_pred_test_digital = np.digitize(y_pred, intervals) - 1
print(y_pred)
print(y_pred_test_digital)
mse = mean_squared_error(y_test_digital, y_pred_test_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_test_digital, y_test_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test_digital, y_pred_test_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
mse = mean_squared_error(y_train_digital, y_pred_train_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_train_digital, y_train_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train_digital, y_pred_train_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
---- ---- ---- [ 0. 30. 60. 90. 120. 150. 180. 210. 240. 270. 300. 330. 360. 390. 420. 450. 480.] [162 141 167 152 162 170 168 166 162 170 152 169 260 138 167 170 157 173 162 99 166 152 162 163 162 378 152 190 140 162 162 166 162 162 190 140 150 180 162 166 157 147 166 170 163 166 152 138 162 202 190 162 190 166 174 190 171 162 190 170 162 162 190 140 147 162 158 138 162 158 199 184] [ 5 4 5 5 5 5 5 5 5 5 5 5 8 4 5 5 5 5 5 3 5 5 5 5 5 12 5 6 4 5 5 5 5 5 6 4 5 6 5 5 5 4 5 5 5 5 5 4 5 6 6 5 6 5 5 6 5 5 6 5 5 5 6 4 4 5 5 4 5 5 6 6] Mean squared error: 1.6805555555555556 Correlation coefficient: 0.45002269860598076 Coefficient of determination (R-squared score, R2 score): 0.09617180205415499 Mean squared error: 1.2814327485380117 Correlation coefficient: 0.46589994996224815 Coefficient of determination (R-squared score, R2 score): 0.10132445839159054
Fixing the reduced class number, I enumerate the original class number to see what a original class number is better.
# independent data
x = group_satcked_green
# dependent data (labels/targets)
y = np.squeeze(stacked_red)
# Split the data into train and test sets
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.05, random_state=42)
# Calculate the minimum and maximum values
infinitesimal = np.finfo(float).eps
min_val = np.min(y) - infinitesimal # to guarantee to include min
max_val = np.max(y) + infinitesimal # to guarantee to include max
print("x_train shape:", x_train.shape)
print("y_train shape:", y_train.shape)
print("x_test shape:", x_test.shape)
print("y_test shape:", y_test.shape)
reduced_class_num = 16
class_num_array = np.arange(reduced_class_num, reduced_class_num * 100 + 1, reduced_class_num)
# class_num_array = np.arange(reduced_class_num * 5, reduced_class_num * 40 + 1, reduced_class_num)
mse_test_list = []
correlation_test_list = []
r_squared_test_list = []
mse_train_list = []
correlation_train_list = []
r_squared_train_list = []
for class_num in class_num_array:
print('---- ---- ----')
print(f'class_num = {class_num}')
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.05, random_state=42)
# Generate class_num+1 evenly spaced intervals
intervals = np.linspace(min_val, max_val, num=class_num+1) # num = class num + 1
# print(intervals)
# Digitize the array to get the indices of the intervals
y_train = np.digitize(y_train, intervals) - 1
y_test = np.digitize(y_test, intervals) - 1
# to see unique elements (see if we have all 0, 1,..., class_num-1 classes, better close to all)
unique_elements = np.unique(y_train)
# print("Unique elements:", unique_elements)
print("Number of unique elements:", len(unique_elements))
model = linear_model.LogisticRegression(fit_intercept=True, max_iter=1000, multi_class='multinomial')
fit_result = model.fit(x_train, y_train)
y_pred = model.predict(x_test)
y_pred_ = model.predict(x_train)
# Define the boundaries for digitization
intervals = np.arange(0, class_num+1, class_num/16)
print(intervals)
y_train_digital = np.digitize(y_train, intervals) - 1
y_test_digital = np.digitize(y_test, intervals) - 1
y_pred_train_digital = np.digitize(y_pred_, intervals) - 1
y_pred_test_digital = np.digitize(y_pred, intervals) - 1
# print(y_pred)
# print(y_pred_test_digital)
print("test eval:")
mse = mean_squared_error(y_test_digital, y_pred_test_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_test_digital, y_test_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_test_digital, y_pred_test_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
mse_test_list.append(mse)
correlation_test_list.append(correlation)
r_squared_test_list.append(r_squared)
print("train eval:")
mse = mean_squared_error(y_train_digital, y_pred_train_digital)
print("Mean squared error:", mse)
correlation = np.corrcoef(y_pred_train_digital, y_train_digital)[0, 1]
print("Correlation coefficient:", correlation)
r_squared = r2_score(y_train_digital, y_pred_train_digital)
print("Coefficient of determination (R-squared score, R2 score):", r_squared)
mse_train_list.append(mse)
correlation_train_list.append(correlation)
r_squared_train_list.append(r_squared)
plot_comparison(y_test, y_pred, f'Logistic Linear Regression Reduced Evaluation {class_num} to {reduced_class_num}, Test Set')
plot_comparison(y_train, y_pred_, f'Logistic Linear Regression Reduced Evaluation {class_num} to {reduced_class_num}, Train Set')
x_train shape: (1368, 5) y_train shape: (1368,) x_test shape: (72, 5) y_test shape: (72,) ---- ---- ---- class_num = 16 Number of unique elements: 13 [ 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.] test eval: Mean squared error: 1.5416666666666667 Correlation coefficient: 0.4453030497739079 Coefficient of determination (R-squared score, R2 score): 0.17086834733893552 train eval: Mean squared error: 1.1608187134502923 Correlation coefficient: 0.44378410042157646 Coefficient of determination (R-squared score, R2 score): 0.1859117170141732
---- ---- ---- class_num = 32 Number of unique elements: 22 [ 0. 2. 4. 6. 8. 10. 12. 14. 16. 18. 20. 22. 24. 26. 28. 30. 32.] test eval: Mean squared error: 1.6944444444444444 Correlation coefficient: 0.4582084037679691 Coefficient of determination (R-squared score, R2 score): 0.08870214752567696 train eval: Mean squared error: 1.1747076023391814 Correlation coefficient: 0.46298174070265335 Coefficient of determination (R-squared score, R2 score): 0.17617136602126982
---- ---- ---- class_num = 48 Number of unique elements: 30 [ 0. 3. 6. 9. 12. 15. 18. 21. 24. 27. 30. 33. 36. 39. 42. 45. 48.] test eval: Mean squared error: 1.8611111111111112 Correlation coefficient: 0.43969624320050904 Coefficient of determination (R-squared score, R2 score): -0.0009337068160597539 train eval: Mean squared error: 1.2478070175438596 Correlation coefficient: 0.4327504506197096 Coefficient of determination (R-squared score, R2 score): 0.12490636079546202
---- ---- ---- class_num = 64 Number of unique elements: 39 [ 0. 4. 8. 12. 16. 20. 24. 28. 32. 36. 40. 44. 48. 52. 56. 60. 64.] test eval: Mean squared error: 1.5416666666666667 Correlation coefficient: 0.4427237599869571 Coefficient of determination (R-squared score, R2 score): 0.17086834733893552 train eval: Mean squared error: 1.1834795321637428 Correlation coefficient: 0.45276394446722484 Coefficient of determination (R-squared score, R2 score): 0.17001956539417284
---- ---- ---- class_num = 80 Number of unique elements: 47 [ 0. 5. 10. 15. 20. 25. 30. 35. 40. 45. 50. 55. 60. 65. 70. 75. 80.] test eval: Mean squared error: 1.6527777777777777 Correlation coefficient: 0.4461650275964236 Coefficient of determination (R-squared score, R2 score): 0.11111111111111116 train eval: Mean squared error: 1.1769005847953216 Correlation coefficient: 0.47426325398766034 Coefficient of determination (R-squared score, R2 score): 0.17463341586449554
---- ---- ---- class_num = 96 Number of unique elements: 53 [ 0. 6. 12. 18. 24. 30. 36. 42. 48. 54. 60. 66. 72. 78. 84. 90. 96.] test eval: Mean squared error: 1.5972222222222223 Correlation coefficient: 0.48152746604882574 Coefficient of determination (R-squared score, R2 score): 0.1409897292250234 train eval: Mean squared error: 1.2149122807017543 Correlation coefficient: 0.45973521922573 Coefficient of determination (R-squared score, R2 score): 0.14797561314707552
---- ---- ---- class_num = 112 Number of unique elements: 61 [ 0. 7. 14. 21. 28. 35. 42. 49. 56. 63. 70. 77. 84. 91. 98. 105. 112.] test eval: Mean squared error: 1.4305555555555556 Correlation coefficient: 0.5105003166926159 Coefficient of determination (R-squared score, R2 score): 0.23062558356676 train eval: Mean squared error: 1.1739766081871346 Correlation coefficient: 0.45996186883524565 Coefficient of determination (R-squared score, R2 score): 0.1766840160735279
---- ---- ---- class_num = 128 Number of unique elements: 68 [ 0. 8. 16. 24. 32. 40. 48. 56. 64. 72. 80. 88. 96. 104. 112. 120. 128.] test eval: Mean squared error: 1.4166666666666667 Correlation coefficient: 0.5145106276111256 Coefficient of determination (R-squared score, R2 score): 0.23809523809523814 train eval: Mean squared error: 1.2185672514619883 Correlation coefficient: 0.4592849257869412 Coefficient of determination (R-squared score, R2 score): 0.14541236288578518
---- ---- ---- class_num = 144 Number of unique elements: 75 [ 0. 9. 18. 27. 36. 45. 54. 63. 72. 81. 90. 99. 108. 117. 126. 135. 144.] test eval: Mean squared error: 1.7083333333333333 Correlation coefficient: 0.4878270961758985 Coefficient of determination (R-squared score, R2 score): 0.08123249299719892 train eval: Mean squared error: 1.2002923976608186 Correlation coefficient: 0.4878416894302014 Coefficient of determination (R-squared score, R2 score): 0.1582286141922371
---- ---- ---- class_num = 160 Number of unique elements: 80 [ 0. 10. 20. 30. 40. 50. 60. 70. 80. 90. 100. 110. 120. 130. 140. 150. 160.] test eval: Mean squared error: 1.4027777777777777 Correlation coefficient: 0.5081518272956013 Coefficient of determination (R-squared score, R2 score): 0.24556489262371617 train eval: Mean squared error: 1.1608187134502923 Correlation coefficient: 0.4853767881800101 Coefficient of determination (R-squared score, R2 score): 0.1859117170141732
---- ---- ---- class_num = 176 Number of unique elements: 85 [ 0. 11. 22. 33. 44. 55. 66. 77. 88. 99. 110. 121. 132. 143. 154. 165. 176.] test eval: Mean squared error: 1.5694444444444444 Correlation coefficient: 0.49056003058201525 Coefficient of determination (R-squared score, R2 score): 0.15592903828197946 train eval: Mean squared error: 1.2485380116959064 Correlation coefficient: 0.47056104507422336 Coefficient of determination (R-squared score, R2 score): 0.12439371074320393
---- ---- ---- class_num = 192 Number of unique elements: 93 [ 0. 12. 24. 36. 48. 60. 72. 84. 96. 108. 120. 132. 144. 156. 168. 180. 192.] test eval: Mean squared error: 1.5972222222222223 Correlation coefficient: 0.4795115105550837 Coefficient of determination (R-squared score, R2 score): 0.1409897292250234 train eval: Mean squared error: 1.1776315789473684 Correlation coefficient: 0.49138666021574107 Coefficient of determination (R-squared score, R2 score): 0.17412076581223745
---- ---- ---- class_num = 208 Number of unique elements: 96 [ 0. 13. 26. 39. 52. 65. 78. 91. 104. 117. 130. 143. 156. 169. 182. 195. 208.] test eval: Mean squared error: 1.6527777777777777 Correlation coefficient: 0.46381682852195877 Coefficient of determination (R-squared score, R2 score): 0.11111111111111116 train eval: Mean squared error: 1.1732456140350878 Correlation coefficient: 0.4915007187113366 Coefficient of determination (R-squared score, R2 score): 0.17719666612578588
---- ---- ---- class_num = 224 Number of unique elements: 99 [ 0. 14. 28. 42. 56. 70. 84. 98. 112. 126. 140. 154. 168. 182. 196. 210. 224.] test eval: Mean squared error: 1.6805555555555556 Correlation coefficient: 0.45002269860598076 Coefficient of determination (R-squared score, R2 score): 0.09617180205415499 train eval: Mean squared error: 1.182748538011696 Correlation coefficient: 0.4664117652507316 Coefficient of determination (R-squared score, R2 score): 0.17053221544643093
---- ---- ---- class_num = 240 Number of unique elements: 107 [ 0. 15. 30. 45. 60. 75. 90. 105. 120. 135. 150. 165. 180. 195. 210. 225. 240.] test eval: Mean squared error: 1.6527777777777777 Correlation coefficient: 0.4477622581118343 Coefficient of determination (R-squared score, R2 score): 0.11111111111111116 train eval: Mean squared error: 1.1805555555555556 Correlation coefficient: 0.4876444824357047 Coefficient of determination (R-squared score, R2 score): 0.1720701656032052
---- ---- ---- class_num = 256 Number of unique elements: 112 [ 0. 16. 32. 48. 64. 80. 96. 112. 128. 144. 160. 176. 192. 208. 224. 240. 256.] test eval: Mean squared error: 1.8333333333333333 Correlation coefficient: 0.46074029714410486 Coefficient of determination (R-squared score, R2 score): 0.014005602240896309 train eval: Mean squared error: 1.182748538011696 Correlation coefficient: 0.5001806407541329 Coefficient of determination (R-squared score, R2 score): 0.17053221544643093
---- ---- ---- class_num = 272 Number of unique elements: 118 [ 0. 17. 34. 51. 68. 85. 102. 119. 136. 153. 170. 187. 204. 221. 238. 255. 272.] test eval: Mean squared error: 1.6527777777777777 Correlation coefficient: 0.4826532902908703 Coefficient of determination (R-squared score, R2 score): 0.11111111111111116 train eval: Mean squared error: 1.2887426900584795 Correlation coefficient: 0.4549296545627164 Coefficient of determination (R-squared score, R2 score): 0.09619795786900975
---- ---- ---- class_num = 288 Number of unique elements: 123 [ 0. 18. 36. 54. 72. 90. 108. 126. 144. 162. 180. 198. 216. 234. 252. 270. 288.] test eval: Mean squared error: 1.5138888888888888 Correlation coefficient: 0.4980726241918156 Coefficient of determination (R-squared score, R2 score): 0.1858076563958917 train eval: Mean squared error: 1.1805555555555556 Correlation coefficient: 0.49649744134825496 Coefficient of determination (R-squared score, R2 score): 0.1720701656032052
---- ---- ---- class_num = 304 Number of unique elements: 128 [ 0. 19. 38. 57. 76. 95. 114. 133. 152. 171. 190. 209. 228. 247. 266. 285. 304.] test eval: Mean squared error: 1.7638888888888888 Correlation coefficient: 0.4798922788412493 Coefficient of determination (R-squared score, R2 score): 0.05135387488328669 train eval: Mean squared error: 1.2485380116959064 Correlation coefficient: 0.47763995189741704 Coefficient of determination (R-squared score, R2 score): 0.12439371074320393
---- ---- ---- class_num = 320 Number of unique elements: 131 [ 0. 20. 40. 60. 80. 100. 120. 140. 160. 180. 200. 220. 240. 260. 280. 300. 320.] test eval: Mean squared error: 1.7222222222222223 Correlation coefficient: 0.4578610120916426 Coefficient of determination (R-squared score, R2 score): 0.07376283846872078 train eval: Mean squared error: 1.246345029239766 Correlation coefficient: 0.46404033191762234 Coefficient of determination (R-squared score, R2 score): 0.1259316608999782
---- ---- ---- class_num = 336 Number of unique elements: 137 [ 0. 21. 42. 63. 84. 105. 126. 147. 168. 189. 210. 231. 252. 273. 294. 315. 336.] test eval: Mean squared error: 1.8194444444444444 Correlation coefficient: 0.41491897039022546 Coefficient of determination (R-squared score, R2 score): 0.02147525676937445 train eval: Mean squared error: 1.2353801169590644 Correlation coefficient: 0.4933076950057393 Coefficient of determination (R-squared score, R2 score): 0.13362141168384933
---- ---- ---- class_num = 352 Number of unique elements: 142 [ 0. 22. 44. 66. 88. 110. 132. 154. 176. 198. 220. 242. 264. 286. 308. 330. 352.] test eval: Mean squared error: 1.8611111111111112 Correlation coefficient: 0.46310627542869415 Coefficient of determination (R-squared score, R2 score): -0.0009337068160597539 train eval: Mean squared error: 1.2521929824561404 Correlation coefficient: 0.4731800075940238 Coefficient of determination (R-squared score, R2 score): 0.1218304604819136
---- ---- ---- class_num = 368 Number of unique elements: 145 [ 0. 23. 46. 69. 92. 115. 138. 161. 184. 207. 230. 253. 276. 299. 322. 345. 368.] test eval: Mean squared error: 1.5555555555555556 Correlation coefficient: 0.5017571314715864 Coefficient of determination (R-squared score, R2 score): 0.1633986928104575 train eval: Mean squared error: 1.222953216374269 Correlation coefficient: 0.4622643321695171 Coefficient of determination (R-squared score, R2 score): 0.14233646257223664
---- ---- ---- class_num = 384 Number of unique elements: 154 [ 0. 24. 48. 72. 96. 120. 144. 168. 192. 216. 240. 264. 288. 312. 336. 360. 384.] test eval: Mean squared error: 1.8055555555555556 Correlation coefficient: 0.42511005537204366 Coefficient of determination (R-squared score, R2 score): 0.028944911297852483 train eval: Mean squared error: 1.263157894736842 Correlation coefficient: 0.4766367538107654 Coefficient of determination (R-squared score, R2 score): 0.11414070969804246
---- ---- ---- class_num = 400 Number of unique elements: 154 [ 0. 25. 50. 75. 100. 125. 150. 175. 200. 225. 250. 275. 300. 325. 350. 375. 400.] test eval: Mean squared error: 1.8194444444444444 Correlation coefficient: 0.4818079423309307 Coefficient of determination (R-squared score, R2 score): 0.02147525676937445 train eval: Mean squared error: 1.2288011695906433 Correlation coefficient: 0.4855109861861982 Coefficient of determination (R-squared score, R2 score): 0.13823526215417203
---- ---- ---- class_num = 416 Number of unique elements: 159 [ 0. 26. 52. 78. 104. 130. 156. 182. 208. 234. 260. 286. 312. 338. 364. 390. 416.] test eval: Mean squared error: 1.9166666666666667 Correlation coefficient: 0.44022126465290107 Coefficient of determination (R-squared score, R2 score): -0.03081232492997188 train eval: Mean squared error: 1.2002923976608186 Correlation coefficient: 0.49459953566695747 Coefficient of determination (R-squared score, R2 score): 0.1582286141922371
---- ---- ---- class_num = 432 Number of unique elements: 165 [ 0. 27. 54. 81. 108. 135. 162. 189. 216. 243. 270. 297. 324. 351. 378. 405. 432.] test eval: Mean squared error: 1.6944444444444444 Correlation coefficient: 0.45616291871853465 Coefficient of determination (R-squared score, R2 score): 0.08870214752567696 train eval: Mean squared error: 1.2383040935672514 Correlation coefficient: 0.48648322507084046 Coefficient of determination (R-squared score, R2 score): 0.13157081147481708
---- ---- ---- class_num = 448 Number of unique elements: 170 [ 0. 28. 56. 84. 112. 140. 168. 196. 224. 252. 280. 308. 336. 364. 392. 420. 448.] test eval: Mean squared error: 1.6527777777777777 Correlation coefficient: 0.4645332380852188 Coefficient of determination (R-squared score, R2 score): 0.11111111111111116 train eval: Mean squared error: 1.2719298245614035 Correlation coefficient: 0.46970184377210306 Coefficient of determination (R-squared score, R2 score): 0.1079889090709455
---- ---- ---- class_num = 464 Number of unique elements: 173 [ 0. 29. 58. 87. 116. 145. 174. 203. 232. 261. 290. 319. 348. 377. 406. 435. 464.] test eval: Mean squared error: 1.6944444444444444 Correlation coefficient: 0.4569813782824711 Coefficient of determination (R-squared score, R2 score): 0.08870214752567696 train eval: Mean squared error: 1.2346491228070176 Correlation coefficient: 0.49020677863046425 Coefficient of determination (R-squared score, R2 score): 0.13413406173610742
---- ---- ---- class_num = 480 Number of unique elements: 180 [ 0. 30. 60. 90. 120. 150. 180. 210. 240. 270. 300. 330. 360. 390. 420. 450. 480.] test eval: Mean squared error: 1.6805555555555556 Correlation coefficient: 0.45002269860598076 Coefficient of determination (R-squared score, R2 score): 0.09617180205415499 train eval: Mean squared error: 1.2814327485380117 Correlation coefficient: 0.46589994996224815 Coefficient of determination (R-squared score, R2 score): 0.10132445839159054
---- ---- ---- class_num = 496 Number of unique elements: 183 [ 0. 31. 62. 93. 124. 155. 186. 217. 248. 279. 310. 341. 372. 403. 434. 465. 496.] test eval: Mean squared error: 1.6666666666666667 Correlation coefficient: 0.4638064243926305 Coefficient of determination (R-squared score, R2 score): 0.10364145658263302 train eval: Mean squared error: 1.2412280701754386 Correlation coefficient: 0.47872261325137877 Coefficient of determination (R-squared score, R2 score): 0.12952021126578472
---- ---- ---- class_num = 512 Number of unique elements: 188 [ 0. 32. 64. 96. 128. 160. 192. 224. 256. 288. 320. 352. 384. 416. 448. 480. 512.] test eval: Mean squared error: 1.5972222222222223 Correlation coefficient: 0.543075386641704 Coefficient of determination (R-squared score, R2 score): 0.1409897292250234 train eval: Mean squared error: 1.2390350877192982 Correlation coefficient: 0.48054044788637845 Coefficient of determination (R-squared score, R2 score): 0.131058161422559
---- ---- ---- class_num = 528 Number of unique elements: 189 [ 0. 33. 66. 99. 132. 165. 198. 231. 264. 297. 330. 363. 396. 429. 462. 495. 528.] test eval: Mean squared error: 1.7916666666666667 Correlation coefficient: 0.42732467268306285 Coefficient of determination (R-squared score, R2 score): 0.036414565826330514 train eval: Mean squared error: 1.2638888888888888 Correlation coefficient: 0.4633726034083941 Coefficient of determination (R-squared score, R2 score): 0.11362805964578437
---- ---- ---- class_num = 544 Number of unique elements: 196 [ 0. 34. 68. 102. 136. 170. 204. 238. 272. 306. 340. 374. 408. 442. 476. 510. 544.] test eval: Mean squared error: 1.7916666666666667 Correlation coefficient: 0.43970398735208555 Coefficient of determination (R-squared score, R2 score): 0.036414565826330514 train eval: Mean squared error: 1.2836257309941521 Correlation coefficient: 0.47881187419459664 Coefficient of determination (R-squared score, R2 score): 0.09978650823481627
---- ---- ---- class_num = 560 Number of unique elements: 198 [ 0. 35. 70. 105. 140. 175. 210. 245. 280. 315. 350. 385. 420. 455. 490. 525. 560.] test eval: Mean squared error: 1.9444444444444444 Correlation coefficient: 0.4596242141160763 Coefficient of determination (R-squared score, R2 score): -0.045751633986928164 train eval: Mean squared error: 1.2858187134502923 Correlation coefficient: 0.4723999346181573 Coefficient of determination (R-squared score, R2 score): 0.098248558078042
---- ---- ---- class_num = 576 Number of unique elements: 205 [ 0. 36. 72. 108. 144. 180. 216. 252. 288. 324. 360. 396. 432. 468. 504. 540. 576.] test eval: Mean squared error: 1.7638888888888888 Correlation coefficient: 0.43285661392592695 Coefficient of determination (R-squared score, R2 score): 0.05135387488328669 train eval: Mean squared error: 1.2894736842105263 Correlation coefficient: 0.4639541511375892 Coefficient of determination (R-squared score, R2 score): 0.09568530781675166
---- ---- ---- class_num = 592 Number of unique elements: 211 [ 0. 37. 74. 111. 148. 185. 222. 259. 296. 333. 370. 407. 444. 481. 518. 555. 592.] test eval: Mean squared error: 1.7777777777777777 Correlation coefficient: 0.4348638505605208 Coefficient of determination (R-squared score, R2 score): 0.043884220354808545 train eval: Mean squared error: 1.2163742690058479 Correlation coefficient: 0.48670768119567076 Coefficient of determination (R-squared score, R2 score): 0.14695031304255934
---- ---- ---- class_num = 608 Number of unique elements: 216 [ 0. 38. 76. 114. 152. 190. 228. 266. 304. 342. 380. 418. 456. 494. 532. 570. 608.] test eval: Mean squared error: 1.6805555555555556 Correlation coefficient: 0.4659531086549822 Coefficient of determination (R-squared score, R2 score): 0.09617180205415499 train eval: Mean squared error: 1.263157894736842 Correlation coefficient: 0.480859721151576 Coefficient of determination (R-squared score, R2 score): 0.11414070969804246
---- ---- ---- class_num = 624 Number of unique elements: 216 [ 0. 39. 78. 117. 156. 195. 234. 273. 312. 351. 390. 429. 468. 507. 546. 585. 624.] test eval: Mean squared error: 1.9722222222222223 Correlation coefficient: 0.42114073752888537 Coefficient of determination (R-squared score, R2 score): -0.06069094304388423 train eval: Mean squared error: 1.2923976608187135 Correlation coefficient: 0.45741126241769076 Coefficient of determination (R-squared score, R2 score): 0.0936347076077193
---- ---- ---- class_num = 640 Number of unique elements: 220 [ 0. 40. 80. 120. 160. 200. 240. 280. 320. 360. 400. 440. 480. 520. 560. 600. 640.] test eval: Mean squared error: 2.0277777777777777 Correlation coefficient: 0.36179838793880814 Coefficient of determination (R-squared score, R2 score): -0.09056956115779635 train eval: Mean squared error: 1.2858187134502923 Correlation coefficient: 0.4628273394227515 Coefficient of determination (R-squared score, R2 score): 0.098248558078042
---- ---- ---- class_num = 656 Number of unique elements: 223 [ 0. 41. 82. 123. 164. 205. 246. 287. 328. 369. 410. 451. 492. 533. 574. 615. 656.] test eval: Mean squared error: 1.6527777777777777 Correlation coefficient: 0.4713022353857203 Coefficient of determination (R-squared score, R2 score): 0.11111111111111116 train eval: Mean squared error: 1.29093567251462 Correlation coefficient: 0.46232912919400926 Coefficient of determination (R-squared score, R2 score): 0.09466000771223548
---- ---- ---- class_num = 672 Number of unique elements: 227 [ 0. 42. 84. 126. 168. 210. 252. 294. 336. 378. 420. 462. 504. 546. 588. 630. 672.] test eval: Mean squared error: 1.9305555555555556 Correlation coefficient: 0.45689655658028855 Coefficient of determination (R-squared score, R2 score): -0.03828197945845013 train eval: Mean squared error: 1.2646198830409356 Correlation coefficient: 0.472065275387751 Coefficient of determination (R-squared score, R2 score): 0.11311540959352628
---- ---- ---- class_num = 688 Number of unique elements: 230 [ 0. 43. 86. 129. 172. 215. 258. 301. 344. 387. 430. 473. 516. 559. 602. 645. 688.] test eval: Mean squared error: 1.9027777777777777 Correlation coefficient: 0.39368855021967386 Coefficient of determination (R-squared score, R2 score): -0.023342670401493848 train eval: Mean squared error: 1.2638888888888888 Correlation coefficient: 0.47872789453046133 Coefficient of determination (R-squared score, R2 score): 0.11362805964578437
---- ---- ---- class_num = 704 Number of unique elements: 239 [ 0. 44. 88. 132. 176. 220. 264. 308. 352. 396. 440. 484. 528. 572. 616. 660. 704.] test eval: Mean squared error: 1.7916666666666667 Correlation coefficient: 0.4081133546510662 Coefficient of determination (R-squared score, R2 score): 0.036414565826330514 train eval: Mean squared error: 1.2295321637426901 Correlation coefficient: 0.47995142043816325 Coefficient of determination (R-squared score, R2 score): 0.13772261210191394
---- ---- ---- class_num = 720 Number of unique elements: 240 [ 0. 45. 90. 135. 180. 225. 270. 315. 360. 405. 450. 495. 540. 585. 630. 675. 720.] test eval: Mean squared error: 1.9722222222222223 Correlation coefficient: 0.4358913822419508 Coefficient of determination (R-squared score, R2 score): -0.06069094304388423 train eval: Mean squared error: 1.4137426900584795 Correlation coefficient: 0.4110594122490662 Coefficient of determination (R-squared score, R2 score): 0.008534798932878451
---- ---- ---- class_num = 736 Number of unique elements: 241 [ 0. 46. 92. 138. 184. 230. 276. 322. 368. 414. 460. 506. 552. 598. 644. 690. 736.] test eval: Mean squared error: 1.5416666666666667 Correlation coefficient: 0.5050029530242061 Coefficient of determination (R-squared score, R2 score): 0.17086834733893552 train eval: Mean squared error: 1.2456140350877194 Correlation coefficient: 0.4687999811551011 Coefficient of determination (R-squared score, R2 score): 0.1264443109522363
---- ---- ---- class_num = 752 Number of unique elements: 249 [ 0. 47. 94. 141. 188. 235. 282. 329. 376. 423. 470. 517. 564. 611. 658. 705. 752.] test eval: Mean squared error: 1.8194444444444444 Correlation coefficient: 0.4690525777068861 Coefficient of determination (R-squared score, R2 score): 0.02147525676937445 train eval: Mean squared error: 1.2719298245614035 Correlation coefficient: 0.4784791515967746 Coefficient of determination (R-squared score, R2 score): 0.1079889090709455
---- ---- ---- class_num = 768 Number of unique elements: 255 [ 0. 48. 96. 144. 192. 240. 288. 336. 384. 432. 480. 528. 576. 624. 672. 720. 768.] test eval: Mean squared error: 1.9861111111111112 Correlation coefficient: 0.36310989106098873 Coefficient of determination (R-squared score, R2 score): -0.06816059757236226 train eval: Mean squared error: 1.3135964912280702 Correlation coefficient: 0.46843563321580156 Coefficient of determination (R-squared score, R2 score): 0.07876785609223513
---- ---- ---- class_num = 784 Number of unique elements: 254 [ 0. 49. 98. 147. 196. 245. 294. 343. 392. 441. 490. 539. 588. 637. 686. 735. 784.] test eval: Mean squared error: 1.7916666666666667 Correlation coefficient: 0.43622657198333903 Coefficient of determination (R-squared score, R2 score): 0.036414565826330514 train eval: Mean squared error: 1.2492690058479532 Correlation coefficient: 0.4683260850364564 Coefficient of determination (R-squared score, R2 score): 0.12388106069094584
---- ---- ---- class_num = 800 Number of unique elements: 254 [ 0. 50. 100. 150. 200. 250. 300. 350. 400. 450. 500. 550. 600. 650. 700. 750. 800.] test eval: Mean squared error: 1.8055555555555556 Correlation coefficient: 0.40623732522034717 Coefficient of determination (R-squared score, R2 score): 0.028944911297852483 train eval: Mean squared error: 1.2638888888888888 Correlation coefficient: 0.4716299005450033 Coefficient of determination (R-squared score, R2 score): 0.11362805964578437
---- ---- ---- class_num = 816 Number of unique elements: 264 [ 0. 51. 102. 153. 204. 255. 306. 357. 408. 459. 510. 561. 612. 663. 714. 765. 816.] test eval: Mean squared error: 1.9861111111111112 Correlation coefficient: 0.4238230770001418 Coefficient of determination (R-squared score, R2 score): -0.06816059757236226 train eval: Mean squared error: 1.3260233918128654 Correlation coefficient: 0.4535445771012145 Coefficient of determination (R-squared score, R2 score): 0.07005280520384782
---- ---- ---- class_num = 832 Number of unique elements: 268 [ 0. 52. 104. 156. 208. 260. 312. 364. 416. 468. 520. 572. 624. 676. 728. 780. 832.] test eval: Mean squared error: 1.6666666666666667 Correlation coefficient: 0.4729213450495393 Coefficient of determination (R-squared score, R2 score): 0.10364145658263302 train eval: Mean squared error: 1.3135964912280702 Correlation coefficient: 0.4649921183679015 Coefficient of determination (R-squared score, R2 score): 0.07876785609223513
---- ---- ---- class_num = 848 Number of unique elements: 268 [ 0. 53. 106. 159. 212. 265. 318. 371. 424. 477. 530. 583. 636. 689. 742. 795. 848.] test eval: Mean squared error: 1.7222222222222223 Correlation coefficient: 0.4546882329512439 Coefficient of determination (R-squared score, R2 score): 0.07376283846872078 train eval: Mean squared error: 1.2616959064327486 Correlation coefficient: 0.4804104142865967 Coefficient of determination (R-squared score, R2 score): 0.11516600980255853
---- ---- ---- class_num = 864 Number of unique elements: 271 [ 0. 54. 108. 162. 216. 270. 324. 378. 432. 486. 540. 594. 648. 702. 756. 810. 864.] test eval: Mean squared error: 1.9444444444444444 Correlation coefficient: 0.3688229638711067 Coefficient of determination (R-squared score, R2 score): -0.045751633986928164 train eval: Mean squared error: 1.2880116959064327 Correlation coefficient: 0.4607349824024031 Coefficient of determination (R-squared score, R2 score): 0.09671060792126784
---- ---- ---- class_num = 880 Number of unique elements: 277 [ 0. 55. 110. 165. 220. 275. 330. 385. 440. 495. 550. 605. 660. 715. 770. 825. 880.] test eval: Mean squared error: 1.9027777777777777 Correlation coefficient: 0.38606130431231317 Coefficient of determination (R-squared score, R2 score): -0.023342670401493848 train eval: Mean squared error: 1.273391812865497 Correlation coefficient: 0.4739358859742344 Coefficient of determination (R-squared score, R2 score): 0.10696360896642931
---- ---- ---- class_num = 896 Number of unique elements: 277 [ 0. 56. 112. 168. 224. 280. 336. 392. 448. 504. 560. 616. 672. 728. 784. 840. 896.] test eval: Mean squared error: 1.7638888888888888 Correlation coefficient: 0.4491387425173966 Coefficient of determination (R-squared score, R2 score): 0.05135387488328669 train eval: Mean squared error: 1.2426900584795322 Correlation coefficient: 0.47145352124873213 Coefficient of determination (R-squared score, R2 score): 0.12849491116126854
---- ---- ---- class_num = 912 Number of unique elements: 284 [ 0. 57. 114. 171. 228. 285. 342. 399. 456. 513. 570. 627. 684. 741. 798. 855. 912.] test eval: Mean squared error: 2.0694444444444446 Correlation coefficient: 0.3286713353263606 Coefficient of determination (R-squared score, R2 score): -0.11297852474323067 train eval: Mean squared error: 1.2931286549707601 Correlation coefficient: 0.45452492527877614 Coefficient of determination (R-squared score, R2 score): 0.09312205755546121
---- ---- ---- class_num = 928 Number of unique elements: 290 [ 0. 58. 116. 174. 232. 290. 348. 406. 464. 522. 580. 638. 696. 754. 812. 870. 928.] test eval: Mean squared error: 1.8194444444444444 Correlation coefficient: 0.4141384900804814 Coefficient of determination (R-squared score, R2 score): 0.02147525676937445 train eval: Mean squared error: 1.202485380116959 Correlation coefficient: 0.5054918407320819 Coefficient of determination (R-squared score, R2 score): 0.15669066403546283
---- ---- ---- class_num = 944 Number of unique elements: 292 [ 0. 59. 118. 177. 236. 295. 354. 413. 472. 531. 590. 649. 708. 767. 826. 885. 944.] test eval: Mean squared error: 1.9166666666666667 Correlation coefficient: 0.37831037130187456 Coefficient of determination (R-squared score, R2 score): -0.03081232492997188 train eval: Mean squared error: 1.2609649122807018 Correlation coefficient: 0.4669473803398881 Coefficient of determination (R-squared score, R2 score): 0.11567865985481662
---- ---- ---- class_num = 960 Number of unique elements: 292 [ 0. 60. 120. 180. 240. 300. 360. 420. 480. 540. 600. 660. 720. 780. 840. 900. 960.] test eval: Mean squared error: 1.9583333333333333 Correlation coefficient: 0.37051266633703217 Coefficient of determination (R-squared score, R2 score): -0.053221288515406195 train eval: Mean squared error: 1.2953216374269005 Correlation coefficient: 0.47384954046268224 Coefficient of determination (R-squared score, R2 score): 0.09158410739868705
---- ---- ---- class_num = 976 Number of unique elements: 300 [ 0. 61. 122. 183. 244. 305. 366. 427. 488. 549. 610. 671. 732. 793. 854. 915. 976.] test eval: Mean squared error: 1.7638888888888888 Correlation coefficient: 0.4178303392856154 Coefficient of determination (R-squared score, R2 score): 0.05135387488328669 train eval: Mean squared error: 1.1900584795321638 Correlation coefficient: 0.49086344589777897 Coefficient of determination (R-squared score, R2 score): 0.16540571492385014
---- ---- ---- class_num = 992 Number of unique elements: 302 [ 0. 62. 124. 186. 248. 310. 372. 434. 496. 558. 620. 682. 744. 806. 868. 930. 992.] test eval: Mean squared error: 1.7638888888888888 Correlation coefficient: 0.43093816661664314 Coefficient of determination (R-squared score, R2 score): 0.05135387488328669 train eval: Mean squared error: 1.2646198830409356 Correlation coefficient: 0.4701594985779692 Coefficient of determination (R-squared score, R2 score): 0.11311540959352628
---- ---- ---- class_num = 1008 Number of unique elements: 306 [ 0. 63. 126. 189. 252. 315. 378. 441. 504. 567. 630. 693. 756. 819. 882. 945. 1008.] test eval: Mean squared error: 2.1666666666666665 Correlation coefficient: 0.30371772737300906 Coefficient of determination (R-squared score, R2 score): -0.1652661064425771 train eval: Mean squared error: 1.3720760233918128 Correlation coefficient: 0.4490251632286824 Coefficient of determination (R-squared score, R2 score): 0.03775585191158892
---- ---- ---- class_num = 1024 Number of unique elements: 304 [ 0. 64. 128. 192. 256. 320. 384. 448. 512. 576. 640. 704. 768. 832. 896. 960. 1024.] test eval: Mean squared error: 1.9027777777777777 Correlation coefficient: 0.37797942443125626 Coefficient of determination (R-squared score, R2 score): -0.023342670401493848 train eval: Mean squared error: 1.2997076023391814 Correlation coefficient: 0.45309109016089966 Coefficient of determination (R-squared score, R2 score): 0.08850820708513851
---- ---- ---- class_num = 1040 Number of unique elements: 312 [ 0. 65. 130. 195. 260. 325. 390. 455. 520. 585. 650. 715. 780. 845. 910. 975. 1040.] test eval: Mean squared error: 1.9305555555555556 Correlation coefficient: 0.3796621809376958 Coefficient of determination (R-squared score, R2 score): -0.03828197945845013 train eval: Mean squared error: 1.307748538011696 Correlation coefficient: 0.4837275705321927 Coefficient of determination (R-squared score, R2 score): 0.08286905651029974
---- ---- ---- class_num = 1056 Number of unique elements: 316 [ 0. 66. 132. 198. 264. 330. 396. 462. 528. 594. 660. 726. 792. 858. 924. 990. 1056.] test eval: Mean squared error: 2.0555555555555554 Correlation coefficient: 0.34656448124174166 Coefficient of determination (R-squared score, R2 score): -0.10550887021475264 train eval: Mean squared error: 1.2916666666666667 Correlation coefficient: 0.4608112848899926 Coefficient of determination (R-squared score, R2 score): 0.0941473576599774
---- ---- ---- class_num = 1072 Number of unique elements: 320 [ 0. 67. 134. 201. 268. 335. 402. 469. 536. 603. 670. 737. 804. 871. 938. 1005. 1072.] test eval: Mean squared error: 1.7361111111111112 Correlation coefficient: 0.4252154709685706 Coefficient of determination (R-squared score, R2 score): 0.06629318394024275 train eval: Mean squared error: 1.1966374269005848 Correlation coefficient: 0.49824566710039364 Coefficient of determination (R-squared score, R2 score): 0.16079186445352744
---- ---- ---- class_num = 1088 Number of unique elements: 318 [ 0. 68. 136. 204. 272. 340. 408. 476. 544. 612. 680. 748. 816. 884. 952. 1020. 1088.] test eval: Mean squared error: 1.7777777777777777 Correlation coefficient: 0.4045666488217864 Coefficient of determination (R-squared score, R2 score): 0.043884220354808545 train eval: Mean squared error: 1.2580409356725146 Correlation coefficient: 0.475614789140867 Coefficient of determination (R-squared score, R2 score): 0.11772926006384898
---- ---- ---- class_num = 1104 Number of unique elements: 323 [ 0. 69. 138. 207. 276. 345. 414. 483. 552. 621. 690. 759. 828. 897. 966. 1035. 1104.] test eval: Mean squared error: 1.8611111111111112 Correlation coefficient: 0.4029068861759726 Coefficient of determination (R-squared score, R2 score): -0.0009337068160597539 train eval: Mean squared error: 1.293859649122807 Correlation coefficient: 0.4594385999256325 Coefficient of determination (R-squared score, R2 score): 0.09260940750320323
---- ---- ---- class_num = 1120 Number of unique elements: 325 [ 0. 70. 140. 210. 280. 350. 420. 490. 560. 630. 700. 770. 840. 910. 980. 1050. 1120.] test eval: Mean squared error: 1.8611111111111112 Correlation coefficient: 0.38371943142152887 Coefficient of determination (R-squared score, R2 score): -0.0009337068160597539 train eval: Mean squared error: 1.2426900584795322 Correlation coefficient: 0.48807596539487264 Coefficient of determination (R-squared score, R2 score): 0.12849491116126854
---- ---- ---- class_num = 1136 Number of unique elements: 331 [ 0. 71. 142. 213. 284. 355. 426. 497. 568. 639. 710. 781. 852. 923. 994. 1065. 1136.] test eval: Mean squared error: 1.6944444444444444 Correlation coefficient: 0.4517964129116188 Coefficient of determination (R-squared score, R2 score): 0.08870214752567696 train eval: Mean squared error: 1.2141812865497077 Correlation coefficient: 0.49809781384805735 Coefficient of determination (R-squared score, R2 score): 0.14848826319933361
---- ---- ---- class_num = 1152 Number of unique elements: 339 [ 0. 72. 144. 216. 288. 360. 432. 504. 576. 648. 720. 792. 864. 936. 1008. 1080. 1152.] test eval: Mean squared error: 2.0 Correlation coefficient: 0.35483220545239 Coefficient of determination (R-squared score, R2 score): -0.07563025210084029 train eval: Mean squared error: 1.3625730994152048 Correlation coefficient: 0.45486328401539844 Coefficient of determination (R-squared score, R2 score): 0.04442030259094387
---- ---- ---- class_num = 1168 Number of unique elements: 336 [ 0. 73. 146. 219. 292. 365. 438. 511. 584. 657. 730. 803. 876. 949. 1022. 1095. 1168.] test eval: Mean squared error: 2.0972222222222223 Correlation coefficient: 0.34319982741955934 Coefficient of determination (R-squared score, R2 score): -0.12791783380018673 train eval: Mean squared error: 1.2792397660818713 Correlation coefficient: 0.4745832664711267 Coefficient of determination (R-squared score, R2 score): 0.1028624085483647
---- ---- ---- class_num = 1184 Number of unique elements: 342 [ 0. 74. 148. 222. 296. 370. 444. 518. 592. 666. 740. 814. 888. 962. 1036. 1110. 1184.] test eval: Mean squared error: 1.8333333333333333 Correlation coefficient: 0.4137347989594087 Coefficient of determination (R-squared score, R2 score): 0.014005602240896309 train eval: Mean squared error: 1.243421052631579 Correlation coefficient: 0.485483682213542 Coefficient of determination (R-squared score, R2 score): 0.12798226110901056
---- ---- ---- class_num = 1200 Number of unique elements: 346 [ 0. 75. 150. 225. 300. 375. 450. 525. 600. 675. 750. 825. 900. 975. 1050. 1125. 1200.] test eval: Mean squared error: 1.9027777777777777 Correlation coefficient: 0.3856102534693767 Coefficient of determination (R-squared score, R2 score): -0.023342670401493848 train eval: Mean squared error: 1.2704678362573099 Correlation coefficient: 0.4891116040869614 Coefficient of determination (R-squared score, R2 score): 0.10901420917546167
---- ---- ---- class_num = 1216 Number of unique elements: 347 [ 0. 76. 152. 228. 304. 380. 456. 532. 608. 684. 760. 836. 912. 988. 1064. 1140. 1216.] test eval: Mean squared error: 1.9166666666666667 Correlation coefficient: 0.37518576343555965 Coefficient of determination (R-squared score, R2 score): -0.03081232492997188 train eval: Mean squared error: 1.1944444444444444 Correlation coefficient: 0.5053984255768346 Coefficient of determination (R-squared score, R2 score): 0.16232981461030171
---- ---- ---- class_num = 1232 Number of unique elements: 347 [ 0. 77. 154. 231. 308. 385. 462. 539. 616. 693. 770. 847. 924. 1001. 1078. 1155. 1232.] test eval: Mean squared error: 1.7777777777777777 Correlation coefficient: 0.4084362837832298 Coefficient of determination (R-squared score, R2 score): 0.043884220354808545 train eval: Mean squared error: 1.2295321637426901 Correlation coefficient: 0.48753829537709903 Coefficient of determination (R-squared score, R2 score): 0.13772261210191394
---- ---- ---- class_num = 1248 Number of unique elements: 352 [ 0. 78. 156. 234. 312. 390. 468. 546. 624. 702. 780. 858. 936. 1014. 1092. 1170. 1248.] test eval: Mean squared error: 2.013888888888889 Correlation coefficient: 0.3399437590796833 Coefficient of determination (R-squared score, R2 score): -0.08309990662931832 train eval: Mean squared error: 1.2448830409356726 Correlation coefficient: 0.477891117240075 Coefficient of determination (R-squared score, R2 score): 0.12695696100449438
---- ---- ---- class_num = 1264 Number of unique elements: 362 [ 0. 79. 158. 237. 316. 395. 474. 553. 632. 711. 790. 869. 948. 1027. 1106. 1185. 1264.] test eval: Mean squared error: 1.9166666666666667 Correlation coefficient: 0.383207539724106 Coefficient of determination (R-squared score, R2 score): -0.03081232492997188 train eval: Mean squared error: 1.2251461988304093 Correlation coefficient: 0.4939207915172938 Coefficient of determination (R-squared score, R2 score): 0.14079851241546248
---- ---- ---- class_num = 1280 Number of unique elements: 356 [ 0. 80. 160. 240. 320. 400. 480. 560. 640. 720. 800. 880. 960. 1040. 1120. 1200. 1280.] test eval: Mean squared error: 1.7361111111111112 Correlation coefficient: 0.4474038384503889 Coefficient of determination (R-squared score, R2 score): 0.06629318394024275 train eval: Mean squared error: 1.3596491228070176 Correlation coefficient: 0.4520649394372574 Coefficient of determination (R-squared score, R2 score): 0.04647090279997623
---- ---- ---- class_num = 1296 Number of unique elements: 366 [ 0. 81. 162. 243. 324. 405. 486. 567. 648. 729. 810. 891. 972. 1053. 1134. 1215. 1296.] test eval: Mean squared error: 1.9722222222222223 Correlation coefficient: 0.3706095612956417 Coefficient of determination (R-squared score, R2 score): -0.06069094304388423 train eval: Mean squared error: 1.2675438596491229 Correlation coefficient: 0.47292463300046395 Coefficient of determination (R-squared score, R2 score): 0.11106480938449392
---- ---- ---- class_num = 1312 Number of unique elements: 368 [ 0. 82. 164. 246. 328. 410. 492. 574. 656. 738. 820. 902. 984. 1066. 1148. 1230. 1312.] test eval: Mean squared error: 1.7777777777777777 Correlation coefficient: 0.40456664882178633 Coefficient of determination (R-squared score, R2 score): 0.043884220354808545 train eval: Mean squared error: 1.2295321637426901 Correlation coefficient: 0.49208731415051526 Coefficient of determination (R-squared score, R2 score): 0.13772261210191394
---- ---- ---- class_num = 1328 Number of unique elements: 370 [ 0. 83. 166. 249. 332. 415. 498. 581. 664. 747. 830. 913. 996. 1079. 1162. 1245. 1328.] test eval: Mean squared error: 1.9444444444444444 Correlation coefficient: 0.36176557943869 Coefficient of determination (R-squared score, R2 score): -0.045751633986928164 train eval: Mean squared error: 1.2887426900584795 Correlation coefficient: 0.45964704856357114 Coefficient of determination (R-squared score, R2 score): 0.09619795786900975
---- ---- ---- class_num = 1344 Number of unique elements: 372 [ 0. 84. 168. 252. 336. 420. 504. 588. 672. 756. 840. 924. 1008. 1092. 1176. 1260. 1344.] test eval: Mean squared error: 1.875 Correlation coefficient: 0.38099053375714387 Coefficient of determination (R-squared score, R2 score): -0.008403361344537785 train eval: Mean squared error: 1.182748538011696 Correlation coefficient: 0.5003685087544218 Coefficient of determination (R-squared score, R2 score): 0.17053221544643093
---- ---- ---- class_num = 1360 Number of unique elements: 371 [ 0. 85. 170. 255. 340. 425. 510. 595. 680. 765. 850. 935. 1020. 1105. 1190. 1275. 1360.] test eval: Mean squared error: 1.7083333333333333 Correlation coefficient: 0.435047042551659 Coefficient of determination (R-squared score, R2 score): 0.08123249299719892 train eval: Mean squared error: 1.2682748538011697 Correlation coefficient: 0.4664945248439736 Coefficient of determination (R-squared score, R2 score): 0.11055215933223583
---- ---- ---- class_num = 1376 Number of unique elements: 377 [ 0. 86. 172. 258. 344. 430. 516. 602. 688. 774. 860. 946. 1032. 1118. 1204. 1290. 1376.] test eval: Mean squared error: 1.8611111111111112 Correlation coefficient: 0.413434161766323 Coefficient of determination (R-squared score, R2 score): -0.0009337068160597539 train eval: Mean squared error: 1.236842105263158 Correlation coefficient: 0.49104931350658143 Coefficient of determination (R-squared score, R2 score): 0.13259611157933315
---- ---- ---- class_num = 1392 Number of unique elements: 383 [ 0. 87. 174. 261. 348. 435. 522. 609. 696. 783. 870. 957. 1044. 1131. 1218. 1305. 1392.] test eval: Mean squared error: 2.0972222222222223 Correlation coefficient: 0.33083959438263544 Coefficient of determination (R-squared score, R2 score): -0.12791783380018673 train eval: Mean squared error: 1.226608187134503 Correlation coefficient: 0.5058904561511268 Coefficient of determination (R-squared score, R2 score): 0.1397732123109463
---- ---- ---- class_num = 1408 Number of unique elements: 382 [ 0. 88. 176. 264. 352. 440. 528. 616. 704. 792. 880. 968. 1056. 1144. 1232. 1320. 1408.] test eval: Mean squared error: 2.0833333333333335 Correlation coefficient: 0.34456362234832855 Coefficient of determination (R-squared score, R2 score): -0.1204481792717087 train eval: Mean squared error: 1.3004385964912282 Correlation coefficient: 0.4601800591879395 Coefficient of determination (R-squared score, R2 score): 0.08799555703288053
---- ---- ---- class_num = 1424 Number of unique elements: 386 [ 0. 89. 178. 267. 356. 445. 534. 623. 712. 801. 890. 979. 1068. 1157. 1246. 1335. 1424.] test eval: Mean squared error: 1.7916666666666667 Correlation coefficient: 0.41574004869527287 Coefficient of determination (R-squared score, R2 score): 0.036414565826330514 train eval: Mean squared error: 1.1710526315789473 Correlation coefficient: 0.5141586856048364 Coefficient of determination (R-squared score, R2 score): 0.17873461628256015
---- ---- ---- class_num = 1440 Number of unique elements: 396 [ 0. 90. 180. 270. 360. 450. 540. 630. 720. 810. 900. 990. 1080. 1170. 1260. 1350. 1440.] test eval: Mean squared error: 1.7777777777777777 Correlation coefficient: 0.41325664650877453 Coefficient of determination (R-squared score, R2 score): 0.043884220354808545 train eval: Mean squared error: 1.185672514619883 Correlation coefficient: 0.4902188114305292 Coefficient of determination (R-squared score, R2 score): 0.16848161523739857
---- ---- ---- class_num = 1456 Number of unique elements: 392 [ 0. 91. 182. 273. 364. 455. 546. 637. 728. 819. 910. 1001. 1092. 1183. 1274. 1365. 1456.] test eval: Mean squared error: 1.8472222222222223 Correlation coefficient: 0.3922657747207214 Coefficient of determination (R-squared score, R2 score): 0.006535947712418277 train eval: Mean squared error: 1.2076023391812865 Correlation coefficient: 0.4945476084131888 Coefficient of determination (R-squared score, R2 score): 0.15310211366965631
---- ---- ---- class_num = 1472 Number of unique elements: 396 [ 0. 92. 184. 276. 368. 460. 552. 644. 736. 828. 920. 1012. 1104. 1196. 1288. 1380. 1472.] test eval: Mean squared error: 1.9027777777777777 Correlation coefficient: 0.39368855021967386 Coefficient of determination (R-squared score, R2 score): -0.023342670401493848 train eval: Mean squared error: 1.2485380116959064 Correlation coefficient: 0.5032400900486917 Coefficient of determination (R-squared score, R2 score): 0.12439371074320393
---- ---- ---- class_num = 1488 Number of unique elements: 402 [ 0. 93. 186. 279. 372. 465. 558. 651. 744. 837. 930. 1023. 1116. 1209. 1302. 1395. 1488.] test eval: Mean squared error: 1.875 Correlation coefficient: 0.41048083566793636 Coefficient of determination (R-squared score, R2 score): -0.008403361344537785 train eval: Mean squared error: 1.2580409356725146 Correlation coefficient: 0.48405756700865465 Coefficient of determination (R-squared score, R2 score): 0.11772926006384898
---- ---- ---- class_num = 1504 Number of unique elements: 404 [ 0. 94. 188. 282. 376. 470. 564. 658. 752. 846. 940. 1034. 1128. 1222. 1316. 1410. 1504.] test eval: Mean squared error: 1.9027777777777777 Correlation coefficient: 0.39678485708741124 Coefficient of determination (R-squared score, R2 score): -0.023342670401493848 train eval: Mean squared error: 1.273391812865497 Correlation coefficient: 0.4896315247523248 Coefficient of determination (R-squared score, R2 score): 0.10696360896642931
---- ---- ---- class_num = 1520 Number of unique elements: 404 [ 0. 95. 190. 285. 380. 475. 570. 665. 760. 855. 950. 1045. 1140. 1235. 1330. 1425. 1520.] test eval: Mean squared error: 1.7916666666666667 Correlation coefficient: 0.40697222497305247 Coefficient of determination (R-squared score, R2 score): 0.036414565826330514 train eval: Mean squared error: 1.1973684210526316 Correlation coefficient: 0.4913412954857841 Coefficient of determination (R-squared score, R2 score): 0.16027921440126935
---- ---- ---- class_num = 1536 Number of unique elements: 408 [ 0. 96. 192. 288. 384. 480. 576. 672. 768. 864. 960. 1056. 1152. 1248. 1344. 1440. 1536.] test eval: Mean squared error: 2.2083333333333335 Correlation coefficient: 0.30649383154711757 Coefficient of determination (R-squared score, R2 score): -0.1876750700280112 train eval: Mean squared error: 1.3245614035087718 Correlation coefficient: 0.47964636775154507 Coefficient of determination (R-squared score, R2 score): 0.07107810530836389
---- ---- ---- class_num = 1552 Number of unique elements: 405 [ 0. 97. 194. 291. 388. 485. 582. 679. 776. 873. 970. 1067. 1164. 1261. 1358. 1455. 1552.] test eval: Mean squared error: 1.7083333333333333 Correlation coefficient: 0.4414361692952945 Coefficient of determination (R-squared score, R2 score): 0.08123249299719892 train eval: Mean squared error: 1.2485380116959064 Correlation coefficient: 0.488534227346123 Coefficient of determination (R-squared score, R2 score): 0.12439371074320393
---- ---- ---- class_num = 1568 Number of unique elements: 413 [ 0. 98. 196. 294. 392. 490. 588. 686. 784. 882. 980. 1078. 1176. 1274. 1372. 1470. 1568.] test eval: Mean squared error: 1.9305555555555556 Correlation coefficient: 0.3582330363535253 Coefficient of determination (R-squared score, R2 score): -0.03828197945845013 train eval: Mean squared error: 1.161549707602339 Correlation coefficient: 0.506796995884191 Coefficient of determination (R-squared score, R2 score): 0.18539906696191522
---- ---- ---- class_num = 1584 Number of unique elements: 417 [ 0. 99. 198. 297. 396. 495. 594. 693. 792. 891. 990. 1089. 1188. 1287. 1386. 1485. 1584.] test eval: Mean squared error: 1.9722222222222223 Correlation coefficient: 0.38708808512121956 Coefficient of determination (R-squared score, R2 score): -0.06069094304388423 train eval: Mean squared error: 1.2551169590643274 Correlation coefficient: 0.4768290483095451 Coefficient of determination (R-squared score, R2 score): 0.11977986027288123
---- ---- ---- class_num = 1600 Number of unique elements: 415 [ 0. 100. 200. 300. 400. 500. 600. 700. 800. 900. 1000. 1100. 1200. 1300. 1400. 1500. 1600.] test eval: Mean squared error: 2.013888888888889 Correlation coefficient: 0.36854770096451805 Coefficient of determination (R-squared score, R2 score): -0.08309990662931832 train eval: Mean squared error: 1.243421052631579 Correlation coefficient: 0.49224819113644336 Coefficient of determination (R-squared score, R2 score): 0.12798226110901056
# plot the trend figures of mse, correlation, and r2
# Create a figure and subplots
fig, (ax1, ax2, ax3) = plt.subplots(3, 1, figsize=(8, 12))
# Plot MSE
ax1.plot(class_num_array, mse_test_list, label='MSE (Test)')
ax1.plot(class_num_array, mse_train_list, label='MSE (Train)')
ax1.set_ylabel('MSE')
ax1.set_xlabel('Original Class Number')
ax1.set_title(f'MSE Curve (reduced class num is {reduced_class_num})')
ax1.legend()
# Plot Correlation
ax2.plot(class_num_array, correlation_test_list, label='Correlation (Test)')
ax2.plot(class_num_array, correlation_train_list, label='Correlation (Train)')
ax2.set_ylabel('Correlation')
ax2.set_xlabel('Original Class Number')
ax2.set_title(f'Correlation Curve (reduced class num is {reduced_class_num})')
ax2.legend()
# Plot R-squared
ax3.plot(class_num_array, r_squared_test_list, label='R-squared (Test)')
ax3.plot(class_num_array, r_squared_train_list, label='R-squared (Train)')
ax3.set_ylabel('R-squared')
ax3.set_xlabel('Original Class Number')
ax3.set_title(f'R-squared Curve (reduced class num is {reduced_class_num})')
ax3.legend()
# Increase the vertical spacing between subplots
plt.subplots_adjust(hspace=0.5)
# Adjust tick, label, title, and legend font sizes
plt.rcParams.update({'font.size': 12})
ax1.tick_params(labelsize=10)
ax2.tick_params(labelsize=10)
ax3.tick_params(labelsize=10)
# Save the figure
plt.savefig(f'mse_correlation_r2_trend_curve_reduced_eval_reduced_class_num_{reduced_class_num}.png', bbox_inches='tight')
# Show the figure
plt.show()
# Convert r_squared_test_list to a NumPy array
r_squared_test_array = np.array(r_squared_test_list)
# Find the index of the maximum value
max_index = np.argmax(r_squared_test_array)
# Get the corresponding class_num value
max_class_num = class_num_array[max_index]
# Print the index and corresponding class_num
print("Max Index:", max_index)
print("Max Original Class Num:", max_class_num)
Max Index: 9 Max Original Class Num: 160
balanced weights don't improve the fitting, but make it worse.
# independent data
x = group_satcked_green
class_num = 48
# dependent data (labels/targets)
y = np.squeeze(stacked_red)
# print(np.max(y), np.min(y))
# Split the data into train and test sets
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.05, random_state=42)
# Calculate the minimum and maximum values
infinitesimal = np.finfo(float).eps
min_val = np.min(y) - infinitesimal # to guarantee to include min
max_val = np.max(y) + infinitesimal # to guarantee to include max
# Generate class_num+1 evenly spaced intervals
intervals = np.linspace(min_val, max_val, num=class_num+1) # num = class num + 1
# print(intervals)
# Digitize the array to get the indices of the intervals
y_train = np.digitize(y_train, intervals) - 1
y_test = np.digitize(y_test, intervals) - 1
print("x_train shape:", x_train.shape)
print("y_train shape:", y_train.shape)
print("x_test shape:", x_test.shape)
print("y_test shape:", y_test.shape)
# to see unique elements (see if we have all 0, 1,..., class_num-1 classes, better close to all)
unique_elements = np.unique(y_train)
print("Unique elements:", unique_elements)
print("Number of unique elements:", len(unique_elements))
x_train shape: (1368, 5) y_train shape: (1368,) x_test shape: (72, 5) y_test shape: (72,) Unique elements: [ 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 29 30 33 34 35 37 42 47] Number of unique elements: 30
# fit
model = linear_model.LogisticRegression(fit_intercept=True, max_iter=1000, class_weight='balanced', multi_class='multinomial')
fit_result = model.fit(x_train, y_train)
print(fit_result.intercept_.shape, fit_result.coef_.shape)
# predict
# Use the trained model to make predictions
y_pred = model.predict(x_test)
# Alternatively, you can get the predicted probabilities for each class
y_prob = model.predict_proba(x_test)
# Print the predicted class labels
print(y_pred, y_test)
print(y_pred.shape, y_test.shape)
# Print the predicted probabilities
# print(y_prob)
(30,) (30, 5) [ 7 7 11 9 8 19 29 21 14 20 14 11 35 13 11 26 13 15 20 9 22 14 8 20 8 37 9 25 29 8 17 21 8 15 19 10 19 26 8 19 9 8 29 26 25 11 14 13 8 27 26 15 25 18 8 14 13 14 14 20 20 13 14 7 9 20 22 13 8 20 29 22] [15 18 16 12 15 13 19 18 16 18 16 15 26 17 18 15 12 17 25 0 17 17 15 13 14 26 18 16 13 13 16 17 14 15 13 12 14 18 17 16 18 12 17 30 19 15 15 18 15 27 14 17 17 16 17 15 15 14 16 17 21 14 16 17 15 19 13 7 20 17 16 18] (72,) (72,)
/usr/local/lib/python3.10/dist-packages/sklearn/linear_model/_logistic.py:458: ConvergenceWarning: lbfgs failed to converge (status=1):
STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.
Increase the number of iterations (max_iter) or scale the data as shown in:
https://scikit-learn.org/stable/modules/preprocessing.html
Please also refer to the documentation for alternative solver options:
https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression
n_iter_i = _check_optimize_result(
accuracy = accuracy_score(y_test, y_pred)
print("Accuracy:", accuracy)
# cm = confusion_matrix(y_test, y_pred)
# print("Confusion Matrix:")
# print(cm)
# the columns represent the predicted labels (predictions)
# the rows represent the true labels (ground truth)
# Predicted Class
# | Class 1 | Class 2 | Class 3 |
# -----------------------------------------------------
# True Class | TP1 | FN1 | FN1 |
# -----------------------------------------------------
# True Class | FP2 | TP2 | FN2 |
# -----------------------------------------------------
# True Class | FN3 | FP3 | TP3 |
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred, y_test)[0, 1]
print("Correlation coefficient:", correlation)
plot_comparison(y_test, y_pred, 'Logistic Linear Regression balanced weights, Test Set')
Accuracy: 0.041666666666666664 Correlation coefficient: 0.4563969713481123
# predict on train
# Use the trained model to make predictions
y_pred_ = model.predict(x_train)
# Alternatively, you can get the predicted probabilities for each class
y_prob_ = model.predict_proba(x_train)
accuracy = accuracy_score(y_train, y_pred_)
print("Accuracy:", accuracy)
# cm = confusion_matrix(y_train, y_pred_)
# print("Confusion Matrix:")
# print(cm)
# the columns represent the predicted labels (predictions)
# the rows represent the true labels (ground truth)
# Predicted Class
# | Class 1 | Class 2 | Class 3 |
# -----------------------------------------------------
# True Class | TP1 | FN1 | FN1 |
# -----------------------------------------------------
# True Class | FP2 | TP2 | FN2 |
# -----------------------------------------------------
# True Class | FN3 | FP3 | TP3 |
# Calculate the correlation coefficient
correlation = np.corrcoef(y_pred_, y_train)[0, 1]
print("Correlation coefficient:", correlation)
plot_comparison(y_train, y_pred_, 'Logistic Linear Regression balanced weights, Train Set')
Accuracy: 0.059941520467836254 Correlation coefficient: 0.38806679746981715
# batch download the plotted figures
# uncomment the code below to download figures if needed
'''
import glob
folder_path = '.'
# file_prefix = 'Comparison (Logistic Linear Regression Reduced Evaluation'
file_prefix = 'Comparison'
# Use glob to find all files with the given prefix in the folder
matching_files = glob.glob(f"{folder_path}/{file_prefix}*")
# print(matching_files)
# # Print the matching file names
# for file_path in matching_files:
# print(file_path)
import zipfile
zip_filename = 'files.zip'
with zipfile.ZipFile(zip_filename, 'w') as zipf:
# Add files to the zip file
for file_path in matching_files:
zipf.write(file_path)
from google.colab import files
files.download(zip_filename)
'''
Use the code cautiously.
# # Specify the path to the root folder
# root_folder = '/content'
# # Get a list of all files in the root folder
# files = os.listdir(root_folder)
# files_to_delete = [file for file in files if file.endswith(".png")]
# for file_ in files_to_delete:
# print(file_)
# # Iterate over the files and delete them
# for file in files_to_delete:
# file_path = os.path.join(root_folder, file)
# if os.path.isfile(file_path):
# os.remove(file_path)